Optics - Diffraction Grating

Light of wavelength 5200 angstroms is incident normally on a transmission diffraction grating with 2000 lines per centimeter. The first-order diffraction maximum is at an angle, with respect to the incident beam, that is most nearly

A. 3^o
B. 6^o
C. 9^o
D. 12^o
E. 15^o

(GR9277 #35)

Solution:

d sin θ = mλ 

λ = 5200 Angstrom = 5200  × 10⁻¹⁰ m = 5.2 × 10⁻⁷ m
d = 1 cm / 2000 = 5 × 10⁻⁴ cm =  5 × 10⁻⁶ m
m = 1

sin θ = mλ / d  =  (5.2 × 10⁻⁷) / (5 × 10⁻⁶) ≈ 0.1

→ arcsin θ = 6^o 

Or, since sin θ ≪ 1 → sin θ ≈ θ 

Convert the angle from radians to degrees: 0.1  × 180/π  ≈ 18/3 =  6^o


Answer: B