If two prisms are combined , as shown in figure, find the total angular dispersion and angle of deviation suffered by a white ray of light incident on the combination.

Explanation

Both prisms will turn the light rays towards their bases and hence in same direction, Therefore turnings caused by both prisms are additive.
Total angular dispersion
`= theta + theta' = (mu_(V) - mU_(R))A + (mu'_(V) - mu'_(R))A'`
`= (1.5 - 1.4) 4^(@) + (1.7 - 1.5) 2^(@) = 1.8^(@)`
Total deviation
`= delta + delta' = ((mu_(V) + mu_(R))/(2) - 1)A + ((mu'_(V) + mu'_(R))/(2) - 1)A' = ((1.5+1.4)/(2)-1) 0.4^(@) + ((1.7 + 1.5)/(2) - 1)0.2^(@)`
`= (1.45-1) 0.4^(@) + (1.6-1)0.2^(@)`
`= 0.45xx0.4^(@) + (1.6 - 1) 0.2^(@)`
`= 0.4xx0.4^(@) + 0.6 xx 0.2^(@)`
`= 1.80+1.2 = 3.0^(@)`