Question 9:
Since for glass, the refractive index depends on wavelength, n = n(λ), white light is dipersed into its constituent wavelengths (colors). Since this is a continuous process there are infinitely many orders.
Question 15:
a) Close spacings d increase the dispersion according to D = m / (d*cosθ).
b) Large number of rulings N increases the resolution according to R = N m.
Exercise 1:
a) d = 21.5*10-3 m / 6140 = 3.50*10-6 m
b) θ = arcsin (mλ/d) = arcsin (1*5.89*10-7m/3.50*10-6m) = 9.7° for m=1. For higher m’s accordingly.
Exercise 2:
d = mλ/sinθ = 2*6.12*10-7m/sin32.2° = 2.30*10-6m è number of rulings N = 2.86*10-2m/2.30*10-6m = 1.24*104 rulings
Exercise 10:
The grating maxima occur for d*sinθ = m*λ with m=0,1,2,3,…
The ruling minima occur for:
a*sinθ = n*λ with n=1,2,3,… or with a=d/2 (opaque and transparent strips of equal width) è d*sinθ = 2n*λ with n=1,2,3,…
è All possible maxima of even numbered order (m=2n) will be absent, since the condition for a minimum is met, i. e. there is destructive rather than constructive interference.
Exercise 20:
D = dθ/dλ = m/(d*cosθ) = m/(d*cosθ) * sinθ/sinθ = m*tanθ/(d*sinθ)
Using d*sinθ = mλ è D = m*tanθ/(m*λ) = tanθ / λ