Question

Light (wavelength, λ = 700 nm) is incident on a barrier containing two slits, as shown. The interference pattern is observed on a screen placed a distance, L = 2 m behind the barrier. If the spacing between adjacent interference maxima is 1 mm, what is the separation, d, between the slits?

Answer 1

To find the separation between the slits in a double-slit interference experiment, the formula dsin(θ) = mλ is used. With the given data of an adjacent maxima spacing of 1mm, a wavelength of 700nm, and a screen distance of 2m, the separation is calculated to be 1.4mm.

Step-by-step explanation:

The question involves calculating the separation (d) between slits in a double-slit interference experiment given the spacing between adjacent interference maxima, wavelength (λ = 700 nm), and the distance from the slits to the screen (L = 2 m). To solve this, we use the double-slit interference formula:

dsin(θ) = mλ

Here m is the order of the maxima, which is 1 for the first maxima, and θ is the angle of the maxima from the central axis. Based on the geometry of the setup, this angle can be approximated by θ = δy / L where δy is the separation between the maxima (1 mm). Thus the formula becomes:

d = mλL / δy

Substituting, we get:

d = (1)(700 x 10-9 m)(2 m) / (1 x 10-3 m) = 1.4 x 10-3 m = 1.4 mm

Therefore, the separation between the slits is 1.4 mm.