Question

Red light of wavelength 633 nmnm from a helium-neon laser passes through a slit 0.400 mmmm wide. The diffraction pattern is observed on a screen 2.90 mm away. Define the width of a bright fringe as the distance between the minima on either side.

Required:
a. What is the width of the central bright fringe?
b. What is the width of the first bright fringe on either side of the central one?

Answer 1

a

`y_1 = 0.004589 \ m`

b

`y_2 =0.009179 \ m`

Step-by-step explanation:

From the question we are told that

The wavelength of the red light is
`\lambda _r = 633 \ nm = 633 *10^(-9) \ m`

The width of the slit is
`d = 0.40 mm = 0.40 *10^(-3) \ m`

The distance of the screen from the point of diffraction is
`D = 2.9 \ m`

Generally the width of the central bright fringe is mathematically represented as

`y_1 = (\lambda * D)/(d)`

=>
`y_1 = (633 *10^(-9) * 2.90 )/(0.40 *10^(-3))`

=>
`y_1 = 0.004589 \ m`

Generally the width of the first bright fringe on either side of the central one is mathematically represented as

`y_2 = 2 * y_1`

=>
`y_2 = 2 * 0.004589`

=>
`y_2 =0.009179 \ m`