A crown glass prism of angle $5^{0}$ is to be combined with a flint glass prism in such a way that the dispersion is zero. Refractive indices for violet and red light are 1.532 and 1.514 respectively for crown glass 1.632 and 1.614 for flint glass. Then angle of flint glass prism is

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$2^{0}$

$10^{0}$

$5^{0}$

${2.5}^{0}$

answer is B.

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Detailed Solution

In question $μ_{ν} = 1.523$

For no dispersion, $\frac{A^{1}}{A} = \frac{μ_{ν} - μ_{r}}{μ_{ν}^{1} - μ_{r}^{1}}$

For crown glass $A = 5^{0}, μ_{ν} = 1.523, μ_{r} = 1.514$ , for flint glass, $μ_{ν}^{1} = 1.632, μ_{r}^{1} = 1.614$

$\frac{A^{1}}{5} = \frac{(1.523 - 1.514)}{(1.632 - 1.614)} \Rightarrow \frac{A^{1}}{5} = \frac{0.009}{0.018} = \frac{1}{2}$ $A^{1} = \frac{5}{2} = {2.5}^{0}$

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