The first order angle of diffraction is 21.2°.
Answer: Option A
Explanation:
It is known that light waves get diffracted through grating will undergo interference fringes. If the wavelength of light is comparable to the diameter of grating then constructive interference will be formed if and only if the diffracted line obey Bragg’s law i.e.,
[tex]n \lambda = d \sin \theta[/tex]
Here d is the grating constant.
[tex]d = \frac{1}{N}[/tex]
Here N is the number of lines per cm.
Hence,
[tex]N=\frac{1}{d} = 6.62 \times 10^{3} \mathrm{cm}^{-1} = 6.62 \times 10^{3} \times 10^{2} \mathrm{m}^{-1}[/tex]
Thus, we get, [tex]\frac{1}{d} = 6.62 \times 10^{5} \mathrm{m}^{-1}[/tex]
Then the diffraction angle θ can be found as below with n=1 as we need to determine the first order diffraction angle. [tex]\sin \theta=\frac{n \lambda}{d}=n \lambda N=1 \times 541.6 \times 10^{-9} \times 6.62 \times 10^{5}=3585.4 \times 10^{-4}=0.3585[/tex]
Thus, obtaining the first- order diffraction angle as,
[tex]\theta = \sin ^{-1} 0.3585 = 21.2^{\circ}[/tex]
