Question

A grating has a line density of 1090 cm⁻¹, and a screen perpendicular to the ray that makes the central peak of the diffraction pattern is 3.5 m from the grating. If light of two wavelengths, 620 nm and 650 nm, passes through the grating, what is the separation on the (flat) screen between the fourth-order maxima for the two wavelengths?

Answer 1

Grating line density, c = 1090 per cm

The distance between two consecutive lines in a grating, d = 1/c = 1 /1090 = 9.17 x 10-4 cm = 9.17 x 10-6 m

Distance between grating and screen, D = 3.5 m

Wavelength, λ1 = 620 nm = 620 x 10-9 m

Wavelength, λ2 = 650 nm = 650 x 10-9 m

Order of maxima, n = 4

The distance of nth maxima for light with λ1 from central maximum on the screen, y1 = nλ1D/d

The distance of nth maxima for light with λ2 from central maximum on the screen, y2 = nλ2D/d

the separation on the screen between the fourth-order maxima for the two wavelengths,

y = y2 – y1 = nD (λ2 – λ1 )/d = 4 x 3.5 x( 650 x 10-9 - 620 x 10-9 )/ 9.17 x 10-6 = 4.58 x 10-2 m

the separation on the screen between the fourth-order maxima for the two wavelengths,

y = 4.58 x 10-2 m