Question

Light from a laser strikes a diffraction grating that has 5 300 grooves per centimeter. The central and first-order principal maxima are separated by 0.488 m on a wall 1.64 m from the grating. Determine the wavelength of the laser light. (In this problem, assume that the light is incident normally on the gratings.)

Answer 1

To solve this problem it is necessary to apply the concepts related to the principle of superposition, as well as to constructive interference. From the definition we know that this can be expressed mathematically as

$sin\theta_m = \frac{m\lambda}{d}$

Where

m = Any integer which represent the number of repetition of spectrum

$\lambda$= Wavelength

d = Distance between slits

From triangle (Watch image below)

$tan\theta_1 = \frac{y_1}{L}$

$tan\theta_1 = \frac{0.488}{1.64}$

$\theta_1 = 16.57\°$

Replacing the angle at the first equation for m=1 we have

$\lambda = d sin \theta_1$

Each of the distances (d) would be defined by

d = \frac{1}{5300} = 0.0001886

$\lambda = (\frac{1}{5300}) sin(16.57)$

$\lambda = 538nm$

Therefore the wavelength of the laser light is 538nm