Question

Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.320 mm wide. The diffraction pattern is observed on a screen 2.60 m away. Define the width of a bright fringe as the distance between the minima on either side.

Answer 1

`W = 10.28\ mm`

Step-by-step explanation:

Given,

Red light wavelength = 633 nm

width of slit = 0.320 mm

distance,d = 2.60 m

Condition of first maximum

`a sin \theta_1 = m\lambda`

`\theta_1 =sin^(-1)((m\lambda)/(a))`

m = 1

`\theta_1 =sin^(-1)((633* 10^(-9))/(0.32* 10^(-3)))`

`\theta_1 = 0.1133^\circ`

Width of the first minima

`y_1 = L tan \theta_1`

`y_1 = 2.60* tan( 0.11331)`

`y_1 = 5.14 \ mm`

Now, width of the central region

`W = 2 y_1`

`W = 2* 5.14`

`W = 10.28\ mm`