[Physics Class Notes] on Interference Fringe Pdf for Exam

Waves have an interference phenomenon that gives rise to interference fringes. In the regions where two of the light waves overlap, the waves’ electric field vectors add up. Light waves having the same polarization can either constructively or destructively interfere. Waves with constructive interference are in the same phase, and those in destructive waves are 180-degree out of space from one another. Furthermore, waves must maintain their phase relationship and be coherent so that the interference does not change with time.

To ensure that two interfering waves have the same polarization, we split a wave into two with the method called division of wavefront. Then the same wave is passed through two closely spaced slits. This article contains a brief description of what is fringe in physics.

Double Slit 

If the light is incident over an obstacle with two smaller slits at a distance d from them, then the wavelets emanating from each of the slits interfere behind that obstacle. Waves passing through each of the slit get diffracted and spread out at the angles where a single slit diffraction pattern results in a nonzero intensity, the waves coming from the slits interferes constructively or destructively. Here is a brief on what is the effect on the interference fringes due to double slit.

If the light falls on a screen kept behind the obstacle, a pattern of dark and bright fringe (stripes) appears on the screen. This pattern of bright and dark lines is called the interference fringe pattern or the interference pattern of light. The brighter lines are the sign of constructive interference, and dark lines indicate destructive interference.

The interference pattern’s central fringe is caused by the constructive interference of light from two slits travelling the same distance to the screen and is bright and destructive if it is dark. The central fringe is known as the zero-order fringe. Crest meets the crest, and trough meets the rough. 

The darker fringes on the sides of the zero-order fringe are the result of destructive interference. Light from one of the slits travels ½ the wavelength longer than the distance that the light from the other slit travels. At these locations, the crests meet the troughs. The first-order fringes then follow these darker fringes. Light from a slit travels a distance one wavelength longer than the distance that the light from the other slit travels. Then again, the crests meet crests.

The interference fringes’ width is most significant at the central fringe of the interference pattern, and then they start decreasing as they move towards the sides.

 

Formulation of Angles for Interference Fringes 

If a light of wavelength λ passes through two slits at a distance d from each other, there will be constructive interference at different angles. We can find these angles by applying the condition for constructive interference, i.e.:

D sinθ = m λ

Here, m = 0, 1, 2, …..

The distance from the slits to the screen differs by the integer number of the wavelengths. Here, crest meets crest.

Now, the angle angles at which the darker fringes can be found (based on the destructive interference condition) are:

D sinθ = (m + ½) λ

Here, m = 0, 1, 2, …..

Now, the distance from the slits to the screen differs by an integer number of wavelength + ½ wavelengths. Here the crest meets the trough.

If we view the interference pattern on a screen at distance L from the slits, the wavelength can be found from the fringes’ spacing. We have sinθ = z/(L2 + z2)½ and λ = zd/(m(L2 + z2)½). Here, z is the distance from the interference pattern’s centre to the pattern’s mth bright light. Now, if L >> z, then (L2 + z2)½ ~ L, and we can write it as:

λ = zd / (mL)

 

Diffraction Gratings 

Diffraction patterns can be created either by a single slit or by double slits. When the light encounters an array of identical and equally-spaced slits, it is known as a diffraction grating. Here, the bright fringe coming from constructive interference from different slits is at the same angles as if they come from two different slits. However, the pattern is just sharper.