Question

Q. A diffraction grating has 3 x 10⁶ lines per meter. The grating is illuminated by monochromatic plane waves of wavelength 600 nm at normal incidence that forms an interference pattern on a screen located 0.50 m away

a) Find the angle the first bright fringe.

b) Find the angle corresponding to the second bright fringe.

c) Find the angle of the third bright fringe.

Answer 1

Solution: Given:- Distance,
d = m 3 x 105
, wavelength,
600nm
.

For first bright fringe the order is given by n=1.

(i) The angle of diffraction normal to grating for first bright fringe is given by:

d quis үхи

$sin\theta = \frac{1\times 600\times 10^{-9}}{\frac{1}{3\times 10^{5}}}$

$sin\theta = 3\times 600\times 10^{-4}$

$sin\theta = 0.18$

$\theta = 10.37^{o}$

(ii) The angle of diffraction normal to grating for second bright fringe is given by:

Here, n=2.

d quis үхи

$sin\theta = \frac{2\times 600\times 10^{-9}}{\frac{1}{3\times 10^{5}}}$

$sin\theta = 6\times 600\times 10^{-4}$

$sin\theta = 0.36$

$\theta = 21.1^{o}$

(iii) The angle of diffraction normal to grating for third bright fringe is given by:

Here, n=3.

d quis үхи

$sin\theta = \frac{3\times 600\times 10^{-9}}{\frac{1}{3\times 10^{5}}}$

$sin\theta = 9\times 600\times 10^{-4}$

$sin\theta = 0.54$

$\theta = 32.68^{o}$