Question

When laser light of wavelength 633.0 nm passes through a diffraction grating, the first bright spots occur at ± 16.8 ∘ from the central maximum.

Part A

What is the line density (in lines/cm) of this grating?

Part B

How many additional pares of bright spots are there beyond the first bright spots?

Answer 1

Part A : What is the line density (in lines/cm) of this grating?

using a formula, we have

N = sin /

where, = wavelength of laser light = 633 x 10^-9 m

then, we get

N = sin 16.8⁰ / (633 x 10^-9 m)

N = 4.56 x 10⁵ lines/m

convert lines/m into lines/cm -

N = 4.56 x 10³ lines/cm

Part B : How many additional pares of bright spots are there beyond the first bright spots?

we know that, m = 1 / N

m = 1 / [(633 x 10^-9 m) (4.56 x 10⁵ lines/m)]

m = 3.46

(3 + first bright spot) = 4 additional