Question

Q1 [30 pts]: Two parallel narrow horizontal slits in an opaque vertical screen are separated center-to-center by 3.8 . These are directly illuminated by a laser system. Horizontal fringes are formed on a vertical viewing screen 4 from the aperture plane. The center of the fourth bright band is 3.5 above the center of the zeroth or central bright band. a. (10 points) Determine the wavelength of the light in air.

Answer 1

Separation between two narrow slits, d = 3.8 mm = 0.0038 m

Distance of the screen from the slits, D = 4 m

Distance of 4th bright band from the central bright band, x = 3.5 cm = 0.035 m

Let λ be the wavelength of light used.

The distance of nth bright fringe from the central bright fringe, x = nλD/d

N = 4 for the fourth bright band

wavelength of light, λ = xd/nD = 0.035 x 0.0038/4x4 = 8.31 x 10-6 m

wavelength of light, λ = 8.31 x 10-6 m

please note:

the units the distance are not given in the question and taken arbitrarily .