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 oppositely 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 . For the first prism, the angular dispersion is: ₁ = ( _ v1 - _ r1 )A = 0.014 5.3^ = 0.0742^ For the second prism, the angular dispersion is: ₂ = ( _ v2 - _ r2 )A' = 0.024 3.7^ = 0.0888^ Since the prisms are joined with their refracting angles oppositely directed, the net angular dispersion is the difference between the individual dispersions: _ net = | ₁ - ₂| _ net = |0.0742^ - 0.0888^ | = 0.0146^