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A deviation o...

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)

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Solution

In achromatic combination, dispersion is zero but deviation is non-zero.
Net deviation is given as: $δ_{n e t} = (μ_{1} - 1) A_{1} - (μ_{2} - 1) A_{2}$ $\Rightarrow 2^{\circ} = 0.5 A_{1} - 0.6 A_{2}$ ...(1)

Condition for dispersion to be zero is given as: $ω_{1} (μ_{1} - 1) A_{1} = ω_{2} (μ_{2} - 1) A_{2}$ $\Rightarrow 0.02 (0.5) A_{1} = 0.03 (0.6) A_{2}$
$\Rightarrow 10 A_{1} = 18 A_{2}$ ...(2)

From equation (1) and (2):
$2^{\circ} = \frac{A_{1}}{2} - \frac{A_{1}}{3}$
$∴ A_{1} = 12^{\circ}$

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