Diffraction grating: A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm. The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90.0° from the central spot. If the experiment were performed with all of the apparatus under water (which has an index of refraction of 1.33), what would be the TOTAL number of bright spots that would show up on the screen?
A) 6
B) 7
C) 12
D) 13
E) 14

Question

Quizplus · Accepted Answer

The equation for the number of bright spots in a diffraction grating pattern is:

N = (d sinθ)/λ

Where N is the number of bright spots, d is the distance between grating lines, θ is the angle between the central maximum and the nth bright spot, and λ is the wavelength of the light.

In this case, we can use the given values to solve for N:

d = 1/3952 cm (since there are 3952 lines per cm)
λ = 514 nm (since the laser light has a wavelength of 514 nm)
n = ? (we need to solve for the maximum value of n that produces a bright spot within the viewing range of ±90.0°)

To find the maximum value of n, we can use the equation for the angle θ:

sinθ = nλ/d

Rearranging, we get:

n = dsinθ/λ

Substituting the values given, we have:

n = (1/3952 cm)(sin 90°)(1.33)/514 nm = 13

Therefore, the total number of bright spots that would show up on the screen is 13, which is answer choice D.

Diffraction Grating: a Thin Beam of Laser Light of Wavelength