Adiffraction 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?

The wavelength of the light is 562.5 nm

Solution:

As per the question:

Order, n = 1

Slit separation, d =

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 = 1

           (1)

Also,

For very small angle, :

≈

Using the above value in eqn (1):