Engineering Physics Multiple Choice Questions on “Resolving Power of Grating”.
1. Which of the following is the correct expression for the resolving power of a grating?
a) (nN + 1)/λ
b) nN/λ
c) nN/λ + 1
d) nN
Answer: d
Clarification: The expression for the resolving power of a grating is given by: (frac{lambda}{partiallambda}) = nN
Hence, it is proportional to the number of slots on the grating and the order of the spectrum. It is independent of the grating constant.
2. What is the SI unit of the Resolving power of a plane transmission grating?
a) m-1
b) cm-1
c) s-1
d) No SI unit
Answer: d
Clarification: Mathematically, the resolving power of a plane transmission grating can be defined as the ratio of the mean wavelength of a pair of spectral lines and the wavelength difference between them. As both the quantities have the same unit, resolving power has no unit.
3. The resolving power of a grating is inversely proportional to the wavelength of the incident light.
a) True
b) False
Answer: a
Clarification: As we know, the resolving power of a grating = nN
Now, n = (e + d) sinΘ / λ, where e + d is the width of the ruled surface of the grating.
Thus, Resolving power = N (e + d) sinΘ / λ.
Hence, the resolving power is inversely proportional to the wavelength of incident light.
4. Our eyes see two objects as separate, only if the angle subtended by them at the eye is greater than _________
a) 30 seconds
b) 1 minute
c) 2 minute
d) 10 seconds
Answer: b
Clarification: Human eyes can see two objects as separate only when the angle subtended by them on the eye is greater than 1 minute. This is the minimum angle of resolution of a normal human eye. This process of observing two objects as separate is called resolution.
5. The resolving power of a grating is directly proportional to grating constant.
a) True
b) False
Answer: b
Clarification: For a grating, the resolving power = nN, where n is the order of the spectrum and N is the total number of slits on the grating. It is independent of the grating constant.
6. If a light is incident on a grating with 5000 lines/cm, then the angular separation of the two lines (5000 Å and 5006 Å) in first order spectrum is ______
a) 0.01°
b) 0.02°
c) 0.03°
d) 0.04°
Answer: b
Clarification: Here, N = 5000. Therefore, a + b = 1/5000 cm
Now we know, (a + b) sinΘ = nλ
For λ = 5000 Å, sinΘ1 = 5 X 10-5 X 5000
Θ1 = 14.47°
For λ = 5006 Å, sinΘ2 = 5.006 X 10-5 X 5000
Θ2 = 14.49°
Angular separation = Θ2 – Θ1 = 0.02°.
7. Light is incident normally on a grating of width 5 X 10-3 m with 2500 lines. What is the resolving power of the grating in the second order spectrum?
a) 2500
b) 5000
c) 1250
d) 500
Answer: b
Clarification: The resolving power of a grating = nN, where n is the order of the spectrum and N is the number of slits on the grating.
Thus, Resolving power = 2 X 2500
= 5000.
8. What is the minimum number of lines per cm in a 2.5 cm wide grating spectrum which will just resolve two sodium lines (5890 Å and 5896 Å) in the first order spectrum?
a) 98
b) 196
c) 392
d) 694
