Question 27
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°
Reference: Past Exam Paper – November 2014 Paper 11 & 12 Q27 &
March 2019 Paper 12 Q29
Note: For March 2019 Paper 12 Q29: 'orange light' instead of 'yellow light'
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 θn = 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°
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