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A thin prism of angle $15^\circ$ made of glass of refractive index $\mu_1 = 1.5$ is combined with another prism of glass of refractive index $\mu_2 = 1.75$. The combination of the prisms produces dispersion without deviation. The angle of the second prism should be
A
$12^\circ$
B
$5^\circ$
C
$7^\circ$
D
$10^\circ$
Detailed Solution
Deviation produced by a thin prism: $\delta = (\mu - 1)A$
For dispersion without deviation, the two prisms are placed oppositely so that their deviations cancel: $\delta_1 = \delta_2$
$(\mu_1 - 1)A_1 = (\mu_2 - 1)A_2$
$(1.5 - 1)\times15^\circ = (1.75 - 1)\times A_2$
$7.5^\circ = 0.75A_2$
$A_2 = 10^\circ$
For dispersion without deviation, the two prisms are placed oppositely so that their deviations cancel: $\delta_1 = \delta_2$
$(\mu_1 - 1)A_1 = (\mu_2 - 1)A_2$
$(1.5 - 1)\times15^\circ = (1.75 - 1)\times A_2$
$7.5^\circ = 0.75A_2$
$A_2 = 10^\circ$