Question

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

slit width on grating (d) = 1/(3*!0^6) m

The equation for interfrence pattern dsin$\theta$ = m$\lambda$

a) For first bright fringe

dsin$\theta1$ = 1$\lambda$

sin$\theta1$ = 600*10^-9 /{1/3*10^6} = 1.8

Not a possible solution

b) for Second bright fringe

d sin$\theta2$ = 2 $\lambda$

sin$\theta2$ = 2* 600*10^-9 /{1/3*10^6} = 3.6

also not a possible solution

c)

for Second bright fringe

d sin
03
= 2 $\lambda$

sin= 2* 600*10^-9 /{1/3*10^6} = 5.4

03

also not a possible solution.

For this grating interefence pattern does not form with this grating.