Light of wavelength 450 nm produces a first-order maximum at 27° when viewed through a grating. At what angle would a first-order maximum occur for a wavelength of 600 nm viewed through this grating?
A) 54°
B) 40°
C) 36°
D) 37°
E) 14°

Question

Quizplus · Accepted Answer

We can use the formula for the grating equation, which is:
dsinθ = mλ
where d is the spacing of the grating (not given), θ is the angle at which the maximum occurs, m is the order of the maximum (1 in this case), and λ is the wavelength of light. 
For the first maximum at 450 nm, we have:
dsin(27°) = (1)(450 nm)
Now we can solve for d:
d = (450 nm) / sin(27°) = 996 nm
Then for the first maximum at 600 nm:
dsinθ = (1)(600 nm)
sinθ = (600 nm) / d
θ = sin⁻¹[(600 nm) / d] = sin⁻¹[(600 nm) / 996 nm] ≈ 37°
Therefore, the answer is D, 37°.

Light of Wavelength 450 Nm Produces a First-Order Maximum at 27°