Question

A diffraction grating produces a first-order bright fringe that is 0.18 m away from the central bright fringe on a flat screen. The separation between the slits of the grating is 2.5 x 10-6 m, and the distance between the grating and the screen is 0.8 m. What is the wavelength of the light shining on the grating?

Answer 1

The wavelength of the light is 562.5 nm

Solution:

As per the question:

Order, n = 1

Slit separation, d =
`2.5* 10^(- 6)\ m`

Distance from the bright fringe, y = 0.18 m

Distance between the screen and the grating, D = 0.8 m

Now,

We know from the eqn for diffraction:

`n\lambda = dsin\theta`

n = 1

`\lambda = dsin\theta` (1)

Also,

For very small angle,
`\theta`:

`sin\theta` ≈
`tan\theta = (y)/(D) = (0.18)/(0.8) = 0.225`

Using the above value in eqn (1):

`\lambda = 2.5* 10^(- 6)* 0.225 = 5.625* 10^(- 7)\ m = 562.5\ nm`