A crown glass prism of refracting angle `6^@` is to be achromatised fro red and blue light using a flint glass prism. Find the angle of flint glass prism and also, the mean deviation from the following data :

Explanation

Here, `A = 6^@, mu_r = 1.520, mu_b = 1.531`
`A' = ?, mu'_r = 1.662, mu'_b = 1.684`
For achromatism, necessary condition is
`(mu_b - mu_r) + (mu'_b - mu'_r) A' = 0`
`(1.531 - 1.520) 6^@ + (1.684 - 1.662) A' = 0`
`:. A' = -(0.011 xx 6)/(0.022) = -3^@`
Negative sign indicates that the two prisms must be joined in opposition.
Now `mu = (mu_r + mu_b)/(2) = (1.520 + 1.531)/(2) = 1.5255`
and `mu' = (mu'_r + mu'_b)/(2) = (1.684 + 1.662)/(2) = 1.673`
Net deviation `=(mu - 1) A + (mu' - 1) A'`
=`(1.5255 - 1) 6^@ + (1.673 - 1)(- 3^@) = 1.134^@`.