Question

The figure shows the interference pattern on a screen 1.0m behind an 800 line/mm diffraction grating. What is the wavelength of the light? 

Answer 1

Concepts and reason

The concept used to solve this problem is constructive interference with diffraction grating.

Initially, use the other maximum interference pattern from the central maximum to find the angle made by the normal with the grating surface.

Finally, use the constructive interference to find the wavelength of light.

Fundamentals

The condition for constructive interference is as follows:

Here, the grating spacing is , the angle made by the normal with the grating surface is , the wavelength is , and the integer is .

The condition for next maximum interference pattern from the central maximum is as follows:

Here, the distance between the first maxima from the central maxima is and the distance between the screen and grating is .

The condition for the next maximum interference pattern from the central maximum is as follows:

Rearrange the above equation for .

$(1)..um=0 $

Substitute for and for L.

The condition for constructive interference is as follows:

The bright spots on both the sides of the central maximum are represented as first order bright fringe.

Therefore, substitute for .

…… (1)

The spacing between two adjacent slits is as follows:

$=P $.

Here, the number of lines in the grating is N.

Substitute for .

Substitute for and for in Equation (1).

Ans:

Thus, the wavelength of the light is .