Question

Consider a grating with 84 lines/mm and 15 mm of illuminated area. Calculate the wavelengths of the first and second order diffraction at a reflective angle of 25 degrees if the angle of incidence is 45 degrees.

Answer 1

This is problem with incident light and it has the form

d = the grating spacing is the inverse of the number of lines per unit length.

Pathdiffernce of incident light is

i = dsin θi

path differencxe of reflected is

r= -dsin θr

Total path difference is

T= dsin θi - (-dsin θr)

T= dsin θi + dsin θr

T= mλ
where m = 0, 1, 2,3...

d = 10^-3/84 = 1.19 x 10^-5 m

1λ = 1.19 x 10^-5 x sin45 + 1.19 x 10^-5 x sin25

λ = 1.19 x 10^-5 x 0.707 + 1.19 x 10^-5 x 0.422

λ = 8.414 x 10^-6 m+ 5.029 x 10^-6 m

λ = 1.344 x 10^-5 m

λ = 13440 x 10^-9 m

λ = 13440 nm this is the wavelength of the first order diffraction

2λ = 1.19 x 10^-5 x sin45 + 1.19 x 10^-5 x sin25

λ = (1.19 x 10^-5 x 0.707 + 1.19 x 10^-5 x 0.422)/2

λ = (8.414 x 10^-6 m+ 5.029 x 10^-6 m)/2

λ = 1.344 x 10^-5 m/2

λ = 6721 x 10^-9 m

λ = 6721 nm this is the wavelength of the second order diffraction