9702/Oct Nov/11/2014/Q27

A diffraction grating experiment is set up using yellow light of wavelength 600 nm. The grating has
a slit separation of 2.00 μm.

What is the angular separation (θ₂ – θ₁) between the first and second order maxima of the yellow
light?

A 17.5°
B 19.4°
C 36.9°
D 54.3°

Solution:

Answer: B.

For a diffraction grating: d sinθ = nλ

Wavelength λ = 600nm = 600×10^-9 m

Slit separation d = 2.00 μm = 2.0×10^-6 m

Angle θ_n = sin^-1 (nλ / d)

When n = 1, θ₁ = sin^-1 ({600×10^-9} / {2.0×10^-6}) = 17.458°

When n = 2, θ₂ = sin^-1 (2 × {600×10^-9} / {2.0×10^-6}) = 36.870°

Angular separation (θ₂ – θ₁) = 36.870 – 17.458 = 19.4°

Reference: PYQ - Oct/Nov 2014 Paper 11 Q27