Diffraction grating: When monochromatic light illuminates a grating with 7000 lines per centimeter, its second order maximum is at 62.4°. What is the wavelength of the light?
A) 336 nm
B) 363 nm
C) 452 nm
D) 633 nm
E) 752 nm

Question

Quizplus · Accepted Answer

The formula to find the wavelength of light is:
d * sinθ = mλ
Where d is the spacing between the grating lines, θ is the angle at which the maximum occurs (in radians), m is the order of the maximum, and λ is the wavelength of the light.

In this case, d = 1/7000 cm (since there are 7000 lines per 1 cm), θ = 62.4° = 1.09 radians (converted from degrees), and m = 2 (since we are looking for the second order maximum).

Plugging these values into the formula, we get:

(1/7000 cm) * sin(1.09 radians) = 2λ

Solving for λ, we get:

λ = (1/2) * (1/7000 cm) * sin(1.09 radians) = 6.33 x 10^-5 cm = 633 nm

Diffraction Grating: When Monochromatic Light Illuminates a Grating with 7000