Calculate the angle of a prism of dispersive power `0.021` and refractive index `1.53` to form an achromatic combination with prism of angle `4.2^@`, and dispersive power `0.045`, having refractive index `1.65`. Find also the net deviation.

Explanation

`{:(omega=0.021,mu=1.53),(omega'=0.045,mu'=1.65),(A'=4.2^(@),):}`
For no dispersion
`omega delta+omega'delta'=0`
or, `omega(mu-1)A+omega'(mu'-1)A'=0`
or, `A=(omega'A'(mu'-1))/(omega(mu-1))=(0.045xx4.2^(@)xx(1.65-1))/(0.021xx(1.53-1))`
Net deviation
`delta+delta'=(mu-1)A+(mu'-1)A'`
`=-11.04^(@)(1.53-1)+4.2^(@)(1.65-1)`
`=-3.12^(@)`