1. A diffraction grating has 4000 lines/cm. The dispersive power of the grating in the third order spectrum in the wavelength region of 5000 Å is _____________
a) 5000
b) 10000
c) 15000
d) 20000
Explanation: We know; the dispersive power of a grating is given by:
\(\frac{\partial \theta}{\partial \lambda}\) = n/(a + b) cosθ
Now, here n = 3 and a + b = 1/5000 cm
Here, sinθ = nλ/(a + b) = 0.6
cosθ = 0.8
Now, \(\frac{\partial \theta}{\partial \lambda}\) = 3 X 4000/0.8
= 15000.
2. Light utilization efficiency of prism and grating respectively is _________
a) High and High
b) High and Low
c) Low and High
d) Low and Low
Explanation: In a grating, the light with the same wavelength is dispersed in several directions as higher-order light. The prism generally has higher light utilization efficiency despite other losses.
3. Wavelength dependency for dispersion is constant for a prism.
a) True
b) False
Explanation: For a prism, the wavelength dependency for a prism is variable. It is high for UV while low for visible light. For a grating, however, it is high and approximately constant.
4. The spectrum observed for a grating is much purer than a prism.
a) True
b) False
Explanation: It is true that the spectrum observed by a plane transmission grating is purer than that of a prism. This is so because for the grating, it is due to diffraction while for the prism, it is due to dispersion.
5. The relationship between the angle of diffraction of violet, θv, and the angle of diffraction for red, θr, for a grating, is ________
a) θv > θr
b) θv < θr
c) θv = θr
d) No relationship
Explanation: For a diffraction grating, the angle of diffraction for violet is less than the one for red. However, with a prism, the angle of deviation for the violet rays of light is more than for the red rays of light.
6. How many spectrums can be achieved by grating and a prism respectively?
a) 1 and 1
b) More than 1 and 1
c) 1 and More than 1
d) More than 1 and More than 1
Explanation: In a grating, a number of spectra can be achieved on the two side of the principal maxima while for a prism, only one spectrum can be obtained.
7. The wavelength range for a grating is _______
a) 200 nm – 400 nm
b) 400 nm – 800 nm
c) 800 nm – 1200 nm
d) 200 – 800 nm
Explanation: For a grating, the wavelength range is from 400 nm to 800 nm. For a prism, the wavelength range is from 365 mm to 920 mm.
8. The phenomenon used for obtaining grating spectra is diffraction. Which phenomenon is used for obtaining prism spectra?
a) Diffraction
b) Interference
c) Scattering
d) Dispersion
Explanation: The prism spectra is obtained by dispersion. It is the splitting of light into seven colors. Violet has the greatest deviation in this case, while for grating spectra violet has the least deviation.
9. 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
Explanation: The expression for the resolving power of a grating is given by: \(\frac{\lambda}{\partial\lambda}\) = 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.
10. 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
Explanation: 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.