Question 322: Ray Optics

Question

A deviation of 2$$^\circ$$ is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass as 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ____________$$^\circ$$ (in degree). (Round off to the Nearest Integer)

Accepted Answer

$${\delta _{net}} = ({\mu _1} - 1){A_1} - ({\mu _2} - 1){A_2}$$
$$2^\circ  = ({\mu _1} - 1){A_1} - ({\mu _2} - 1){A_2}$$ ....... (1)
and $${\omega _1}({\mu _1} - 1){A_1} = {\omega _2}({\mu _2} - 1){A_2}$$ ..... (2)
Substituting the values in equation (1) and (2), we get
$$2^\circ  = 0.5{A_1} - 0.6{A_2}$$ ...... (3)
$$10{A_1} = 18{A_2}$$ ...... (4)
From equation (3) and (4)
$$2^\circ  = {{{A_1}} \over 2} - {{{A_1}} \over 3}$$
$${A_1} = 12^\circ $$

Ray Optics

Choose the correct answer: