As the colour of light varies from red to violet, the refractive index of a material M₁ changes by 0.014 , while that of another material M₂ changes by 0.024 . Two thin prisms, one constructed from M₁ ( A = 5.3^ ) and the other from M₂ ( A' = 3.7^ ), are joined with their refracting angles similarly directed. Determine the angular dispersion produced by this combination.

Step-by-step solution

The angular dispersion produced by a thin prism is given by = ( _v - _r)A = A . For the first prism, the angular dispersion is: ₁ = ₁ A₁ = 0.014 5.3^ = 0.0742^ For the second prism, the angular dispersion is: ₂ = ₂ A₂ = 0.024 3.7^ = 0.0888^ Since the two prisms are joined with their refracting angles similarly directed, their individual angular dispersions will add up. Total angular dispersion = ₁ + ₂ = 0.0742^ + 0.0888^ = 0.163^