Category: Physics Notes PPT

The ability of a lens to bend the light falling on it is called the power of a lens. Since the lens of shorter focal length will bend the light rays more will have more power. A convex lens converges the light rays towards the principal axis whereas a concave lens diverges the light rays away from the principal axis. 

Here,

[P=frac{1}{F}]      

          

The power of a lens is defined as the inverse of its focal length (f) in meters (m).

Power of a Lens Formula Definition

The power of a lens is specified as [P=frac{1}{F}], where f is the focal length.

The S.I. unit of power of a lens is [m^{-1}].  This is also known as diopter.

The focal length (f) of a converging lens is considered positive and that of a diverging lens is considered negative. Thus, the power of a converging lens is positive and that of the diverging lens is negative.

Lens Formula in Terms of Power

Fig.1 shows two lenses L1 and L2 placed in contact. The focal lengths of the lenses are f1 and f2, respectively. Let P be the point where the optical centres of the lenses coincide (lenses being thin). 

Now, let us place an object ‘O’ beyond the focus of lens L1 such that OP = u (object distance) on the common principal axis (coaxially). 

Here, the first lens L1 alone forms an image at I1 where PI1 = v1 (image distance). 

Also, this point I1 works as the virtual object for the second lens L2 and the final image is formed at I, at a distance PI = v. The ray diagram (Fig.1) formed by the combination of two convex lenses has the following attributes:

u  = Object-distance for the first lens

v =  final image-distance for the second lens

v1 = image-distance for the first image I1 for the first lens. As the lenses are pretended to be thin, v1 is also the object distance for the second lens.

The lens formula for the image I1 formed by lens L1 will be

[frac{1}{v_1}-frac{1}{u}=frac{1}{F}]…..(1) 

The equation for the image formation for the second lens L2:

[frac{1}{v}-frac{1}{v_1}=frac{1}{f_2}]…..(2) 

Adding eq (1) and (2):

[frac{1}{v_1}-frac{1}{u}+frac{1}{v}-frac{1}{v_1}=frac{1}{F_1}+frac{1}{f_2}]

[frac{1}{v}-frac{1}{u}=frac{1}{F_1}+frac{1}{f_2}]…..(3) 

The focal length of the combined lens is given by-

If the combination is replaced by a single lens of focal length F such that it forms the image of O at the position I,

1/v – 1/ u =  1/ F……(4)

This type of lens is called the equivalent lens for the combination.

Combining (3) and (4),

1/F = 1 / f1 + 1/ f2……(5)

Here, F is the focal length of the equivalent lens for the combination. As the power of a lens is P =  1/ F, eq (5) immediately gives, 

The power of any number of lenses in contact is equal to the algebraic sum of the power of two individual lenses. This is true for any situation involving two thin lenses in contact.

How to Find the Power of the Lens Using the Focal Length?

The power of a lens is measured as the reciprocal of the focal length of the lens.

Relation with focal length: A lens of less focal length produces more converging or diverging and is said to have more power.

I.e.,

According to the lens maker’s formula,

Since, P = 1/ F 

We get,

Here, 

v = refractive index of the material

R1 = Radius of curvature of the first surface of the lens

R2 =  Radius of curvature of the second surface of the lens

For a converging lens, power is taken as positive and for a diverging lens, power is taken as negative.

Definition for the Power of Lens Unit

The S.I. the unit of power is dioptre (D).

When f = 1 meter, P = 1/ f = 1/ 1 = 1 dioptre

Hence, one dioptre is the power of a lens of focal length one meter.

When f is in 1 cm, P = 1/ f / 100 = 100/ f

So, we get the formulas to describe the relationship between P and f,

Optical Power (Lens Power)

Optical power is defined as the degree to which a lens, mirror, or other optical system converges or diverges the light. Optical power is also referred to as dioptric power, convergence power, refractive power, or refractive power. It is equal to P = 1/ f.

Dioptre Formula 

The Dioptre formula is used to calculate the optical power of a lens or curved mirror. The dioptre is the unit for a measure of the refractive index of a  lens. The power of a lens is specified as the inverse of the focal length in meters, or D =1/ f, where D is the power in dioptres.

Power of Lens Calculation: Solved Example

1. Find the power of a plano-convex lens, when the radius of a curved surface is 15 cm and v =1.5.

Solution: Given  R1 = ∞, R2 = – 15 cm, v= 1.5 cm

P = [frac{1}{f}=(v-1)(frac{1}{R_1}-frac{1}{R_2})]

   = (1.5-1)[(frac{1}{infty }+frac{1}{0.15})]

   = 0.5[times frac{1}{0.15}=3.33]

From the above formula for the power of the lens, we understand that the power of a lens is the reciprocal of the focal length (which we calculate in metres). Lens power is measured in dioptres (D), which is also equal to 1/m. 

Converging (convex) lenses have positive focal lengths, so they also have positive power values. However, diverging (concave) lenses have negati
ve focal lengths, so they also have negative power values.

In Physics terminology, you must have heard about scalar and vector quantities. We often define any physical quantity by magnitude. Hence the physical quantity featured by magnitude is called a scalar quantity. That’s it! But there are also physical quantities that have a certain specific magnitude along with the direction. Such a physical quantity represented by its magnitude and direction is called a vector quantity. Thus, by definition, the vector is a quantity characterized by magnitude and direction. Force, linear momentum, velocity, weight, etc. are typical examples of a vector quantity. Unlike scalar quantity, there is a whole lot to learn about vector quantity.

Before learning about the vector quantities and their properties, let us differentiate between the scalar quantities and vector quantities.

Scalar Quantities

• These are the quantities that have only magnitude and no direction. 

• The scalar quantities are one-dimensional.

• With the change in magnitude, scalar quantities also change.

• The mathematical operation is done between the two or more scalar quantities results in a scalar quantity. 

• Simple alphabets are used to denote scalar quantities.

• Example – speed, time, mass, volume, etc.

Vector Quantities

• These quantities have both magnitude and direction.

• They can be one, two or three-dimensional. 

• The vector quantities change when both magnitude and direction are changed.

• The resultant of two or more vector quantities is a vector quantity when mathematical operations are applied.

• To denote these quantities, an arrowhead is made above the alphabets.

• Example – displacement, force, velocity, acceleration, etc. 

Vectors are denoted by an arrow marked over a signifying symbol. For example,

[overrightarrow{a}] or [ overrightarrow{b}] [ overrightarrow{b}]

The magnitude of the vector [overrightarrow{a}] and [overrightarrow{b}] is denoted by ∥a∥ and ∥b∥ , respectively. 

Examples of the vector are force, velocity, etc. Let’s see below how it is represented 

Velocity vector:

[overrightarrow{v}]

Force vector:

[overrightarrow{F}]

Linear momentum:

[overrightarrow{p}]

Acceleration vector:

[overrightarrow{a}]

Force is a vector because the force is the magnitude of intensity or strength applied in some direction. Velocity is the vector where its speed is the magnitude in which an object moves in a particular path.

Classification Of Vectors 

There are various types of vectors that are used in Physics and Mathematics. Beneath are the names and descriptions of these vectors:

• Zero Vector – It is the type of vector whose magnitude is equal to zero.

• Position Vector – The vector which describes the position of a point in a cartesian system with respect to the origin is known as the position vector. 

• Unit Vector – The magnitude of this vector is equal to unity.

• Like Vectors – Like vectors are the vectors having the same direction.

• Unlike Vectors – These are the vectors having opposite directions.

• Co-initial Vectors – The co-initial vectors have the same starting point.

• Equal Vectors – The vectors which have the same magnitude, as well as the direction, are said to be equal vectors.

• Coplanar Vectors – Coplanar vectors are the vectors that are parallel to the same plane or lie in the same plane.

• Collinear Vectors – These are the vectors that are parallel to each other irrespective of their magnitudes and direction are known as collinear vectors. 

• Negative of a Vector – The two vectors having the same magnitude but different directions (opposite direction) are said to be the negative vectors of each other. 

• Displacement Vector – It is the vector that represents the displacement of a point from one position to another.  

Two-Dimensional Vectors Depiction

Two- dimensionally vectors can be represented in two forms, i.e. geometric form, rectangular notation, and polar notation.

1. Geometric Depiction of Vectors

In regular simple words, a line with an arrow is a vector, where the length of the line is the magnitude of a vector, and the arrow points the direction of the vector. 

2. Rectangular Depiction

In this form, the vector is placed on the  x and y coordinate system as shown in the image 

The rectangular coordinate notation for this vector is 

[overrightarrow{v}] = (6,3). An alternate notation is the use of two-unit vectors î = (1,0) and ĵ = (0,1) so that v = 6î + 3ĵ.

3. Polar Depiction

In the polar notation, we specify the vector magnitude r, r≥0, and angle θ with the positive x-axis. 

Now we will read different vector properties detailed below.

Equality of Vectors

If you compare two vectors with the same magnitude and direction are equal vectors. Therefore, if you translate a vector to position without changing its direction or rotating, i.e. parallel translation, a vector does not change the original vector. Both the vectors before and after changing position are equal vectors. Nevertheless, it would be best if you remembered vectors of the same physical quantity should be compared together. For example, it would be practicable to equate the Force vector of 10 N in the positive x-axis and velocity vector of 10 m/s in the positive x-axis.

Vector Addition

Think of two vectors a and b, the
ir sum will be a + b. 

The image displays the sum of two vectors formed by placing the vectors head to tail. 

Vector addition follows two laws, i.e. Commutative law and associative law.

A. Commutative Law – the order

in which two vectors are added does not matter. This law is also referred to as parallelogram law. Consider a parallelogram, two adjacent edges denoted by a + b, and another duo of edges denoted by, b + a. Both the sums are equal, and the value is equal to the magnitude of diagonal of the parallelogram

Image display that parallelogram law that proves the addition of vector is independent of the order of vector, i.e. vector addition is commutative

B. Associative Law – the addition of three vectors is independent of the pair of vectors added first.

(a+b)+c=a+(b+c).

Vector Subtraction

First, understand the vector -a. It is the vector with an equal magnitude of a but in the opposite direction.

The image shows two vectors in the opposite direction but of equal magnitude.

Therefore, the subtraction of two vectors is defined as the addition of two vectors in the opposite direction.

x – y = x + (-y)

Vector Multiplication by a Scalar Number

Consider a vector [overrightarrow{a}] with magnitude ∥a∥ and a number ‘n’. If a is multiplied by n, then we receive a new vector b. Let us see. Vector [overrightarrow{b}]= n  [overrightarrow{a}]   The magnitude of the vector  [overrightarrow{b}]   is ∥na∥. 

The direction of the vector [overrightarrow{b}] is the same as that of the vector a [overrightarrow{a}]

If the vector [overrightarrow{a}] is in the positive x-direction, the vector b [overrightarrow{b}] will also point in the same direction, i.e. positive x-direction.

Suppose if we multiply a vector with a negative number n whose value is -1. Vector [overrightarrow{b}] will be in the opposite direction of the vector [overrightarrow{a}]

The Vector Product 

The cross product of two vectors is equal to the product of the magnitude of the two given vectors and sine of the angle between these vectors. The vector product is represented as 

A x B = |A| |B| sin θ nˆ

 

Where,

A and B are two vectors

|A| = magnitude of vector A

|B| = magnitude of vector B

θ = angle between the vectors A and B

 

[hat{n}] = unit vector perpendicular to the plane containing the two vectors

 

Some properties of the vector product are discussed below:

A x B ≠ B x A 

But, A x B = (-B) x A

A x (B + C) = A x B + A x C

• When the vectors are perpendicular to each other then the vector product is maximum. 

• Due to parallel and anti-parallel vectors, the cross product becomes zero.

• When a vector gets multiplied by itself, then it results in a zero vector. 

• The orthogonal unit vectors show the cross product in the following manner,

           i x i = j x j = k x k = 0

           i x j = k, j x k = i, k x i = j

           j x i = -k, k x j = -i, i x k = -j

 

Fun Facts

1. Do you know, scalar representation of vector quantities like velocity, weight is speed, and mass, respectively?

2. Scalar multiplication of vector fulfills many of the features of ordinary arithmetic multiplication like distributive laws

a(x + y) = xa + xb(a + b)y = ay + by 1x = x(−1)x = -x₀a = 0

Quasars are among the brightest and most distant objects known to man. These astronomical objects of high luminosity are found in the centre of galaxies and shine so brightly that the brightest quasar in the universe can outshine all of the stars in their galaxy. A Quasar is powered by gas spiralling at velocities approaching the speed of light into an extremely large black hole. These black holes are a billion times as massive as our sun.

Quasar is among the brightest celestial objects that are crucial to the understanding of our early universe. Quasars are so luminous that they are visible even at a distance of billion light-years. A quasar is also known as a quasi-stellar object which is an extremely luminous galactic nucleus surrounded by a gaseous disk. The most distant and biggest quasar in the quasar universe is the J0313-1806, which has a mass of 1.6 billion times our sun and dates back to 670 million years ago after the Big Bang.

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Early Discovery and History

Around the 1930s, a physicist with bell and telephone laboratories, Karl Jansky discovered static interference on the transatlantic lines coming from the Milky Way. But it was only in the 1950s, these luminous objects were discovered by the early radio surveys of the sky. Most radio sources were identified as normal-looking galaxies but some, however, coincided with objects which appeared to be blue in colour and photographs showed them to be embedded in faint and fuzzy halos.  

Due to their starlike appearance, these luminous objects were termed “quasi-stellar radio sources” which was later changed to Quasar in 1964. But the optical spectra of Quasar represented a new mystery that was solved by a Dutch American astronomer by the name of Maarteen Schmidt in 1963. 

Maarteen discovered the pattern of the emission lines in the brightest Quasar 3C273 , coming from hydrogen atoms that had a redshift of 0.158. Redshift means the shifting of the emission lines towards the longer redder wavelengths because of the expansion of the universe. 

The wavelength of each emission line was 1.158 times longer than that measured in the laboratory and a redshift of this magnitude placed the 3C273 more than two billion light-years away according to Hubble’s law.  Nothing so bright had been ever seen at a distance so far away.  An even surprising finding was the significant variation in the brightness of these quasars, which implied that the total size of the quasar can’t be more than a few light-days across. 

The Quasar galaxy is galaxies with supermassive black holes. Quasar can only live in a galaxy with supermassive black holes. The Quasar galaxy also exhibits properties common to the other active galaxies. 

The Conundrum About Quasar 

The astronomers were faced with a difficult problem: how could an object about the size of the solar system have a mass of about a million stars and can outshine by 100 times a galaxy of a hundred billion stars. 

The answer was shortly proposed after Schmidt’s discovery by Russian astronomers Yakov Zel’dovich, Igor Novikov and Austrian American astronomer Edwin Salpeter who gave the right answer to the problem – accretion by gravity onto supermassive black holes. 

The redshift controversy was settled in the early 1980s that the fuzzy halos surrounding some of the quasars are starlight from the galaxy hosting the quasar and that these galaxies are at high redshifts.

Structure of the Quasar

In some of the quasar, gas tumbles into the deep gravitational well of the black hole which piles up in a rapidly rotating “accretion disk” close to the black hole. Other than accretion disk and supermassive black holes, quasars have other features as well such as clouds of gas that move at high velocities around the inner structure. Some quasars also have radio jets, which emit beams of radiation at X-ray and radio wavelengths.

The largest quasar in the quasar universe is formally designated J1107 + 2115 and has been given the Hawaiian name, Poniua’ena. 

Conclusion

Quasars are highly luminous objects which allow astronomers to understand the evolution of galaxies. The further the quasar is, it takes a longer time for light to reach us. So, any quasar billions of light-years old will provide information about life billions of light-years ago.  

If the position of an object changes with respect to time and its surroundings, the body is said to be in motion. Mathematically, motion can be described with displacement, velocity, and acceleration in a particular frame of reference. The motion of a particle can be classified on the basis of its trajectory, the simplest being motion along a straight line namely rectilinear motion. The displacement, velocity, and acceleration vectors are restricted to one dimension. Rectilinear motion has three types: uniform motion (zero acceleration), uniformly accelerated motion (non-zero constant acceleration), and motion with non-uniform acceleration. Examples of rectilinear motion are free-fall under gravity and the simple harmonic motion of a mass attached to a spring.

Rectilinear Motion definition

If a particle is restricted to move along a straight line, its motion is called rectilinear (or linear) motion. Such a motion can be described using one coordinate only. Displacement of the particle and its derivatives i.e. velocity and acceleration all are one-dimensional vectors. Free-fall under the Earth’s gravitational field, a car moving along a straight path can be approximated as rectilinear motions. 

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Mathematical Form of the Motion

To qualitatively study a rectilinear motion, a one-dimensional reference frame consisting of an axis (X-axis) and an origin at O (x = 0) is considered.

Position, distance and displacement: The position of a particle is a vector quantity which points from the origin to the particle. Its magnitude is given by the distance between them. When the particle is set into motion, it follows a path so that the position changes with time. Displacement is the vector difference of the position after an interval of time and it points from the initial position to the final position. Distance is the total path traversed along the trajectory whereas displacement is the shortest path. If the position of the particle changes from xi  to xf in time  Δt, the displacement is given by, 

x = xf – xi 

Speed and Velocity: Rate of change of distance is called speed and the time rate of change of displacement is called velocity. Speed is a scalar but velocity is a vector having direction same as displacement. Instantaneous velocity at a time t is given by,

[v = frac{d}{dt} x]

Acceleration: If velocity changes with time, the time rate of change is defined as acceleration. It is also a vector,

[a = frac{dupsilon}{dt} = frac{d^2x}{dt^2}]

Since all the vectors are restricted to one dimension, it is enough to consider the magnitudes only. 

Graphical Representation

If position is plotted as a function of time, the graph shows the trajectory of the particle. Velocity at any instant is given by the slope of this graph since velocity is the time derivative of position. Acceleration is the time derivative of velocity so it is given by the slope of velocity versus time graph.

Rectilinear Motion Formulas Derivation

Considering different values of acceleration, rectilinear motion can be categorised into three types which are: uniform rectilinear motion, uniformly accelerated motion and motion with non-uniform acceleration.

Uniform Rectilinear Motion Definition: It describes a motion along a straight line with zero acceleration. The velocity of the particle does not change with time such that,

[frac{dupsilon}{dt}  = 0] 

[upsilon = upsilon_0]

[upsilon_0]  is the constant velocity. From the above equation, 

[frac{dupsilon}{dt}  = upsilon_0] 

[int_{x_0}^x dx = upsilon_0 int_0^t dt]

[x(t) = x_0 + upsilon_0 t]

[x(t) = x_0 + upsilon_0 t]

Here, x₀  is the initial position of the particle i.e.  x(t=0) = x0 

Clearly, the trajectory of the particle is a straight line with a constant slope v₀ and y intercept x₀. The position-time and velocity-time graphs are shown below.

Uniformly Accelerated Rectilinear Motion Definition: If the acceleration is constant at a value a0 i.e. a=a0 

[frac{dupsilon}{dt} = a_0]

The initial velocity and displacement are v0 and x0 respectively i.e. 

v(t=0) = v0x (t=0) = x0

Integrating the last equation,

[int_{upsilon_0}^{upsilon} dupsilon = a_0 int_{0}^{t} dt]

v(t) = v0 + a0t

So, velocity varies linearly with time if the acceleration is constant.

Substituting v = dxdt in the expression of v,

 dxdt = v0 + a0t

Performing integration on both sides,

[int{x}{x_0} dx  = a_0 int_{0}^{t} tdt + int_{upsilon_0}^{upsilon} dupsilon ]

[x(t) = x_0 + upsilon_0 t + frac{1}{2} a_0 t^2]

For constant acceleration, the expression of displacement is quadratic in time.

Time can be eliminated from the expressions of velocity and displacement by substituting t=v –v0 a0 in the expression of displacement,

[x = x_0 + (frac{upsilon – upsilon_0}{a_0}) (upsilon_0 frac{upsilon – upsilon_0}{2})]

[x(t) = x_0 + (upsilon_0 frac{upsilon – upsilon_0}{a_0}) + frac{1}{2} a_0( frac{upsilon – upsilon_0}{a_0})^2 ]

[x = x_0 + upsilon^2 –  frac{upsilon_0^2}{2a_0}]

[upsilon^2 = upsilon_0^2 + 2a_0 (x – x_0) ]

This equation relates the position and velocity at any arbitrary instant. Since acceleration is constant in time, it can be represented as a straight line parallel to the time axis. Velocity is also linear, but it varies with time so that it is a straight line with a nonzero slope. Displacement is quadratic in time and the trajectory is parabolic.

Motion with Non Uniform Acceleration: Acceleration changes with time and position in these motions. Simple harmonic motion is an example where the magnitude of the acceleration is proportional to position. The trajectory of an SHM is sinusoidal. 

Example

Free fall under gravity: If the gravitational acceleration got an object due to the Earth’s gravitational attraction is considered to be constant over the distance of interest, free fall of an object in the gravitational field of Earth can be approximated as a rectilinear motion with constant acceleration. Any nonconservative force like air resistance, viscosity< /a> is considered to be absent in the problem.

If an object falls freely from a height h above the ground under gravity, its initial height d(t = 0) is h and initial velocity v(t = 0) is zero. The constant acceleration is g = 9.8 m/s2 . Using the expressions of position and velocity,

Velocity at any instant t is, 

v(t)=gt

Displacement at any instant t is,

d(t)=12gt2

This displacement from the initial height is downwards such that the height of the object decreases with time.

Did you know?

The motion of two particles under the action of a central force (e.g. electrostatic force) can be approximated as a rectilinear motion.

Free-fall under the Earth’s gravitational field is not actually a rectilinear motion because of the rotation of the Earth. The Coriolis force, due to the rotation, causes the free-fall trajectory to bend.

Linear motion and rotation (on a plane) about an axis have similar dynamics. 

Places like museums, retail stores, and even buildings require linear motion control.

Joule is the S.I. unit of heat (which is a form of energy and also a derived unit of energy and is a measure of doing work or generating heat) generally represented by “J”. It is equal to the energy transferred to a body when 1 N force acts on it to displace it by 1 m in the direction of the force.

Calorie and Joule

1 Calorie is the amount of heat required at a pressure of 1 standard atmosphere to raise the temperature of 1gram (g) of water through 1 degree Celsius. 

Joule and Calorie both are units of heat or energy variously defined. The relation between Joule and Calorie can easily be depicted with a simple formula i.e. 

1 calorie (cal) = 4.184 (approx 4.2) Joule, which is wholly elaborated in this article 

How to Convert Joule into Calorie?  

For International use, caloric is defined as the amount of heat required to raise the temperature of 1 gram (g) of water from 14.5 degrees Celsius to 15.5 degrees Celsius. 

Joules (J) and calories (Cal) are the most widely used energy and heat units. For joule calorie conversion it becomes more daunting tasks for the conversion of 1 joule to Calorie because it involves the division of the coefficient with a hectic value of 0.2390057361. It is quite a bit easier to convert Calorie into Joule as it involves the multiplication of coefficient with 4.18.

Quick Conversion Chart of Joule into Calories

What is the Relation between Calorie and Joule? 

As we know, energy is the ability to do work. Heat is also a form of energy. Both heat and energy can be measured using multiple units, and calories and joules are also examples of such heat units. 

And as you know, the relation between Calorie and Joule is proportional to each other which means that any change in the Calorie (cal) will also lead to a change in its equivalent value in joules (J). It also implies that Joule (J) is directly proportional to Calorie (cal) which means that:

• When the value in terms of Calorie (cal) increases, then its value in Joule (J) increases at a rate of 4.2.

• When the value in terms of Calorie (cal) decreases, then its value in joules (J) decreases at a rate of 4.2.

Calories to Joules Formula

As you know, Calorie (cal) and Joule (j) are the most important physical quantities in physics. Hence, the conversion between Calorie and Joule and vice versa is crucial in solving Physics numerical. So scroll down to get the list consisting of various commonly used quantities.

Quick Grasp on Calorie to Joule Table

Do you Know?

We use calories in food instead of joules, and you will be able to know the answer by reading the text below.

1 joule is the work required to exert 1 Newton (N) force on a body for a distance of about 1 meter (m). Also, it equals the energy of 1 watt (W) of power for 1 second (sec).

A calorie is the amount of energy needed to raise 1 gram of water temperature by 1 degree Celsius.

So, it seems more logical to use calories based on its definition as a unit of energy; it seems to be more reliable to use it as a unit of energy in the case of food energy. A larger calorie is used as food energy.

Uses of Joule and Calorie

The concept of joules and calories is used in many fields. Some of them are as follows:

(i) Nutritional sciences

In the context of nutrition, calorie is the most commonly used unit of energy. Here, the larger calorie called the kilocalorie is used. Energy of a system/ component is measured as the number of kilocalories (kcal) of nutritional energy.

However, different physiologists and nutritionists in different parts of the world have different preferences; for example, in the United States, most nutritionists prefer the unit kilocalorie to the unit kilojoules, whereas most physiologists prefer to use kilojoules. In many countries of the world, nutritionists prefer the kilojoule to the kilocalorie. US food labeling laws (designed by USFDA) mandate the use of kilocalories (under the name of “Calories”); kilojoules are permitted to be included on food labels alongside kilocalories, but not required to do so. Contrary to this, in Australia, kilojoule is the officially preferred unit even when kilocalories, to some extent retains itself in popular use. 

In order to deal with misinterpretations between specific energy or energy density figures and energy; energy density is always quoted as “calories per serving” or “kcal per 100 g”, while nutritional requirements are often expressed in calories or kilocalories per day.

The major macronutrients in food (carbohydrate, protein and fat) contain 4 kilocalories per gram (carbs.), protein contains approximately 4 kcal/g  and 9 kcal in fats. Alcohol also has an energy value of 7 kcal/g. 

(ii) Chemistry

In other scientific fields, the term calorie almost always refers to the small calorie. and even though it is not an SI unit, it is still used in chemistry. For example, the
energy released in a chemical reaction per mole of reagent is sometimes denoted in kilocalories per mole. The main purpose here for the use of calorie was the ease with which it could be calculated in laboratory reactions, especially in aqueous solutions, for example,  when a volume of reagent is dissolved in water forming a solution, (concentration in moles per liter (1 liter weighing 1 kilogram)), it will induce a temperature change in degrees Celsius in the total volume of water solvent, that can be easily calculated in calories. It is also sometimes useful in specifying energy quantities related to reaction energy, such as enthalpy of formation and the size of activation barriers.

(iii) Measurement of energy content of food

The calorie, when defined  initially, was meant to specifically measure energy in the form of heat, especially in experimental calorimetry.

In many past experiments, a bomb calorimeter would be used to determine the energy content of food by burning a food sample and measuring the temperature change in the surrounding water. Today, this method has been replaced by calculating the energy content indirectly from adding up the energy provided by energy-containing nutrients of food (such as protein, carbohydrates, and fats). 

(iv) One joule represents many scientific measurements such as:

• The amount of electricity required to run a one watt device for 1 second or the energy required to bring an acceleration of one kg mass at 1 m/s² through a distance of 1 meter distance.

• In energy calculations, especially heat energy, it is measured as the energy required to raise the temperature 0.239 g of water from 0°C to 1°C, or from 32°F to 33.8°F.

• Another example is the typical energy that is released as heat by a person at rest every 1/60 s (17 ms) is one joule.

• The kinetic energy of a 2 kg mass traveling at 1 m/s is also one joule (based on calculations).

Wavelength is considered as the measure of the length of a wave cycle, which is complete entirely. The velocity of a wave is considered as the distance travelled by a particular point on the wave. Generally, if you randomly take any wave, the wavelength and velocity relation will be witnessed as proportionate. This relation is expressed by using the wave velocity formula. This formula was derived in order to explain the relation between velocity and wavelength. In this article, we will have a brief discussion regarding velocity,  wavelength and how they are related to each other. We will discuss the velocity wavelength formula for better understanding.

 

Velocity

The velocity of an object is considered as the rate of change of the position of the object with respect to a particular frame of time and reference. To some, it might sound complicated and surprising, but velocity is basically speeding up a particular object in the same direction. Velocity is considered as a vector quantity because to define velocity; one needs both the direction and magnitude of the object or the wave. The SI unit of velocity got fixed as a metre per second (m/s). If you witness a change in the direction or magnitude in the velocity of a particular object, then it is believed that the object is accelerating at a certain speed.

 

Initial and Final Velocity

Initial velocity is defined as the speed at which an object travels when an initial force is applied to the object by gravity. On the other hand, the final velocity is considered as a vector quantity because it is considered as the measure of the speed and direction of a moving object when the object has reached its maximum acceleration point.

 

Constant Velocity

The motion with a constant velocity from the initial stage is considered the simplest form of motion. Normally constant velocity gets witnessed whenever an object slides over a horizontal or low surface that has a bit of friction. For example, when a puck slides over a hockey rink.

 

Wavelength

Wavelength is considered as the property of a wave in which the total distance between two identical points of two successive waves is measured or calculated. Wavelength is denoted by the Greek letter Lambda. So, the total distance that gets calculated between the trough of one wave and the next wave is known as the wavelength.

 

 

The wavelength of light is defined as the distance that exists between two successive crests or troughs of the light waves.

 

The Wavelength of Visible Light

• The wavelength of visible light, when calculated, ranges between 400 nm to 700 nm. From here, you can also learn and know about the wavelengths of different colours that got extracted from the spectrum.

• The spectrum of visible light is believed to have different colours which have different wavelengths.

• The violet colour that comes out of the spectrum has the shortest wavelength, whereas the red colour has the longest wavelength.

 

Relation Between Velocity and Wavelength of Light

It is considered that for any wave when you multiply the wavelength with the frequency of the wave, it gives the velocity of the wave. This formula was given mathematically by the wave velocity formula.

 

V = f × λ

Where,

V = The velocity of the wave, which gets measured using m/s

f = The frequency of the wave which gets measured using Hz

λ = The wavelength of the wave which gets measured using m

Amplitude, frequency, wavelength and velocity are considered as characteristics of a wave. In the case of a constant frequency, the wavelength is directly proportional to the velocity. This property is derived by 

 

V ∝ λ

To explain this relation between wavelength and velocity of light, let’s discuss some examples.

• In a situation when the frequency is constant if the wavelength of a wave gets doubled, then automatically, the velocity of the wave also gets doubled. 

• In a situation when the frequency remains constant, if the wavelength of the wave increases four times from its original position, then the velocity of the wave will also increase four times.

Hence, this is a brief explanation of velocity and wavelength relation. I hope you understand every point and concept so that it can help you in the near future.

The Most Important Characteristics of Waves are Listed Below.

1. Amplitude: The amplitude of a wave is a measurement of how far it has moved from its resting position. On the graph below, the amplitude is depicted. In most cases, the amplitude is measured by looking at a wave graph and calculating the height of the wave from its resting point. The amplitude of a wave is a measurement of its strength or intensity. When looking at a sound wave, for example, the amplitude will indicate how loud the sound is. The amplitude of the wave affects the energy of the wave in a direct proportion.

2. Wavelength: A wave’s wavelength is the distance between two corresponding positions on back-to-back cycles. This can be calculated by measuring the distance between two wave crests or troughs. In physics, the wavelength is commonly denoted by the Greek letter lambda (λ).

3. Period and Frequency: The frequency of a wave is the number of times it cycles each second. Hertz, or cycles per second, is the unit of frequency measurement. The lower case “f” is frequently used to signify frequency. The time between wave crests is known as the wave period. The length of the period is expressed in seconds. The upper case “T” is commonly used to indicate the period. The frequency and the period are inextricably linked. The frequency is one over the period, and the period is one over the frequency. As indicated in the formulas below, they are reciprocals of each other. T = 1/f or period = 1/frequency f = 1/T or frequency = 1/period.

4. Speed: Wave velocity is the rate at which a wave travels. Another significant characteristic of a wave is its propagation speed. This is the rate at which the wave’s disturbance moves. The speed of mechanical waves is determined by the medium through which they travel. Sound, for example, travels at a different pace in water t
   han it does in air. The letter “v” is commonly used to denote a wave’s velocity. By multiplying the frequency by the wavelength, the velocity may be computed. v = f * wavelength or velocity = frequency * wavelength