1. The resolving power of a grating is inversely proportional to the wavelength of the incident light.
a) True
b) False
Explanation: 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.
2. 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
Explanation: 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
3. The resolving power of a grating is directly proportional to grating constant.
a) True
b) False
Explanation: 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
4. 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°
Explanation: 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°.
5. 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
Explanation: 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.
6. 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
Explanation: Now, we know that for a grating \(\frac{\lambda}{d\lambda}\)=nN
λmean = 5893 Å = 5.89 X 10-7 m
d λ = 6 Å = 6 X 10-10m
n = 1, N = ?
So , N = \(\frac{\lambda}{n Xd\lambda}\) = 982
No of lines per cm = 982/2.5 = 392.
7. A grating has 16000 per inch over a length of 5 inches. What will be the smallest wavelength difference for a light of wavelength 6000 Å?
a) 0.01 Å
b) 0.02 Å
c) 0.03 Å
d) 0.04 Å
Explanation: N = 16000 X 5 = 80000, n = 2
Wavelength = 6 X 10-5cm
Resolving power = nN = 2 X 80000 = 160000
Smallest wavelength difference = λ/nN
= 0.0375 Å.
8. A linearly polarized wabe is always __________
a) In x-y plane
b) A Transverse wave
c) A Longitudinal wave
d) In y-z plane
Explanation: A linearly polarized is always a transverse wave, i.e., the displacement of each point is always at right angles to the direction of propagation of the wave.
9. The direction in which the electric vectors oscillate in a polarized wave is called as _______
a) Polarizing axis
b) Plane of polarization
c) Pass axis
d) Propagating axis
Explanation: When a light wave is polarized, the electric vectors along the direction of propagation are absorbed by the polaroid. Thus, the electric vectors oscillate perpendicular to the propagation of wave. This direction is known as pass axis.
10. Sound waves can be polarized.
a) True
b) False
Explanation: Longitudinal waves cannot be polarized as their direction is the same as its vibration. Thus, it’s intensity will not change as it passes through a rotating analyzer.