Question

a. How many lines per millimetre are required in a grating if the first-order diffraction line at 500 nm is to be observed at a reflection angle of 10 deg when the angle of incidence is 60 deg?

I got 2080 line/mm for this part, which is the right answer! need help with part b

b. What wavelength would have a second-order diffraction line at the same position as (a)? Your answer should have units of nanometers (nm).

Answer 1

(a) The relation between wavelength (2) and spacing between reflecting surfaces (d) is, ni=d(sin i+sinr For first order diffraction n=1. ni=d (sin i +sin r) (1) 500 nm = d (sin 60° +sin10) 500 nm (sin 60° +sin 109) = 480.92 nm The number of lines per millimeter, , line 10 nm 1 mm = 2080 lines/mm | 480.92 nm mm (6) The wavelength would have a second order diffraction line is, For second order = 2. (2)1=d sin 60°+sin 10°) 480.92 nm (sin 60° + sin 109) 1 = 250 nm