Anarrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 1.00-cm-thick flat piece of crown glass and back to air again. the beam strikes at a 30.0° incident angle.
(a) at what angles do the two colors emerge?
(b) by what distance are the red and blue separated when they emerge?

Answer

given,

wavelength of red light = 660 nm

wavelength of blue light = 470 nm

thickness = 1 cm = 0.01 m

angle of incident = 30°

using Snell's law

n₁ sin θ₁ = n₂ sin θ₂

refractive index for red and blue color for crown glass

n_r = 1.512     n_b = 1.524

now,

incident ray is red

when incident ray is blue

so,

on solving

similarly for blue ray the angle of emerge is 30°

b)

now, refracting angle of blue and red ray

for blue ray

now,

 d₁ = 1 x tan(19.316°) = 0.3505 m

 d₂ = 1 x tan (19.158°) = 0.3474 m

now, the distance is separated by

  Δ d = d₁ - d₂

  Δ d = 0.3505 - 0.3474

 Δ d =0.0031 cm

see earlier