A diffraction grating has 5500 linescm When a beam of monoc

A diffraction grating has 5500 lines/cm . When a beam of monochromatic light goes through it, the second pair of bright spots occurs at ±26.0 cm from the central spot on a screen 42.0cm past the grating.

Part A

What is the wavelength of this light?

Part B

How far from the central spot does the next pair of bright spots occur on the screen?

Solution

N = 5500 lines/cm = 550000 lines/m

d = 1 / N = 1.82 * 10^-6 m

a) m = 2

tan phi₂ = x₂ / L = 26 / 42 = 0.619

phi₂ = tan^-1 (0.619) = 31.76 deg

sin phi₂ = sin 31.76 = 0.526

d sin phi = m lambda

d sin phi₂ = 2 lambda

lambda = d sin phi₂ / m = 1.82 * 10^-6 * 0.526 / 2

= 4.79 * 10^-7 m

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b) m = 3

d sin phi₃ = 3 lambda

sin phi₃ = 3 lambda / d = 3 * 4.79 * 10^-7 / 1.82 * 10^-6

= 0.789

phi₃ = sin^-1 (0.789) = 52.09 deg