Question Detail
Question
A diffraction grating has 4000 lines per cm. The angle between the central maximum and the third order maximum is 36°. What is the wavelength of the light?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The grating spacing d = 1/N = 1/4000 cm = 2.5 × 10⁻⁴ cm = 2.5 × 10⁻⁶ m. For the third order maximum (m=3): d sin θ = mλ. sin 36° = 0.5878. λ = (d sin θ)/m = (2.5e-6 × 0.5878)/3 = 1.4695e-6/3 = 4.898e-7 m = 489.8 nm ≈ 490 nm.
Hint
Use d sin θ = mλ. d = 1/N.