Question

Light shines through a single slit whose width is 5.7 × 10-4 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 4.2 mm. What is the wavelength of the light?

Answer 1

Step-by-step explanation:

It is given that,

Slit width,
`d=5.7* 10^(-4)\ m`

A diffraction pattern is formed on a flat screen located 4.0 m away, L = 4 m

The distance between the middle of the central bright fringe and the first dark fringe is 4.2 mm, y = 4.2 mm = 0.0042 m

Let
`\lambda` is the wavelength of the light.

Using condition of diffraction as,

`d\ sin\ \theta=n\lambda`

`\lambda=(d\ sin\theta)/(n)`..............(1)

Also,
`tan\theta=(y)/(L)`

`\theta=tan^(-1)((y)/(L))=tan^(-1)((0.0042)/(4))=0.060`

`\lambda=(5.7* 10^(-4)\ sin(0.060))/(1)`

`\lambda=596\ nm`

So, the wavelength of the light is 596 nm. Hence, this is the required solution.