Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.24 m from the grating. in the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.20 mm . what is the difference between these wavelengths? answer in meters.

The difference between these wavelengths is 15.85 nm.

Explanation:

Given that,

The number of lines on the grating N= 900 cm

Distance between screen grating L= 2.24 m

Order number = 1

Distance y = 3.20 mm

We need to calculate the width of the slit

Using formula of width

Put the value into the formula

We need to calculate the angular distance

The angular separation for different wavelength  is

We know that,

Linear separation is

We nee to calculate the difference between these wavelengths

Put the value into the formula of angular separation

Hence, The difference between these wavelengths is 15.85 nm.