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

Answer:

The wavelength of the light is 562.5 nm

Solution:

As per the question:

Order, n = 1

Slit separation, d = $2.5\times 10^{- 6}\ m$

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, $\theta$:

$sin\theta$ ≈ $tan\theta = \frac{y}{D} = \frac{0.18}{0.8} = 0.225$

Using the above value in eqn (1):

$\lambda = 2.5\times 10^{- 6}\times 0.225 = 5.625\times 10^{- 7}\ m = 562.5\ nm$