Question

1. (a) Consider light with a wavelength of 535 nm is passing through a diffraction grating with 924 lines per cm. At what distance from the central bright maximum will the 1^st order maximum be seen on a screen placed 1.20 m from the diffraction grating. Give your answer in centimeters (cm) with 3 significant figures.

(b) Unpolarized light with an intensity of 25.0 units is passed through two successive polarizing filters, the first with its polarization axis aligned with the vertical and the second with its polarization axis rotated 62 from the vertical. Find the intensity of the light after passing through the two polarizing filters. Give your answer in same unit as the original light and with 3 significant figures.

Answer 1

Given:

Wavelength of light, = 535 nm = 535 × 10^-7 cm

Number of lines per cm, N = 924

Distance between slits, d = 1/N = 1/924

Distance from the grating to the screen, D = 1.2m = 120 cm

Constructive interference (brightness) will occur if the difference in their two path lengths is an integral multiple of their wavelength () i.e., difference = n where n = 1, 2, 3, ...

For n = 1, we have first diffraction maximum

Position of 1st order principal maximum from central maximum, y = D /d

y =( 120 * 535 * 10^-7 )/(1/924)

y = 59320800 × 10^-7

y = 5.93 cm

1st order maximum will be seen at a distance of 5.93 cm from central bright maximum.