A low-pressure sodium vapor lamp whose wavelength is 5.89 x 10−7 m passes through double-slits that are 6.7 x 10−4 m apart and produces an interference pattern whose fringes are 3.2 x 10−3 m apart on the screen. What is the distance to the screen?

2.7 meters
3.0 meters
3.6 meters
4.2 meters

3.6 meters

Explanation:

The formula that gives the position of the maxima on the distant screen for double-slit diffraction is

where

m is the order of the maximum

is the wavelength of the source

D is the distance of the screen

d is the distance between the slits

The distance between two consecutive fringes is therefore given by

where in this problem, we have:

is the wavelength of the source

is the distance between the slits

is the distance between the fringes

Therefore, solving the equation for D, we find the distance to the screen: