What is the angular separation of two spectral lines of wavelengths 417 nm and 388 nm formed in order m = 2 with a 456 line/mm grating?
A)1.63°
B)1.52°
C)0°

Question

Quizplus · Accepted Answer

Using the grating equation, we can find the angle of diffraction for each wavelength:
θ = sin^(-1) (mλ/d)

For λ = 417 nm and m = 2, θ = sin^(-1) (2(417x10^(-9) m)/(456 lines/mm x 10^(-3) m)) = 30.09°
For λ = 388 nm and m = 2, θ = sin^(-1) (2(388x10^(-9) m)/(456 lines/mm x 10^(-3) m)) = 28.46°

The angular separation between the two wavelengths can be found by taking the difference:
Δθ = 30.09° - 28.46° = 1.63°

Therefore, the answer is A) 1.63°.

What Is the Angular Separation of Two Spectral Lines of Wavelengths