Optics Question 95

Question: An achromatic prism is made by crown glass prism $ (A _{c}=19^{o}) $ and flint glass prism $ (A _{F}=6^{o}) $ . If $ ^{C}{\mu _{v}}=1.5 $ and $ ^{F}{\mu _{v}}=1.66 $ , then resultant deviation for red coloured ray will be

Options:

A) 1.04°

B) 5°

C) 0.96°

D) 13.5°

Show Answer

Answer:

Correct Answer: D

Solution:

For achromatic combination $ {\omega _{C}}=-{\omega _{F}} $

$ {{[({\mu _{v}}-{\mu _{r}})A]} _{C}}=-{{[({\mu _{v}}-{\mu _{r}})A]} _{F}} $

$ \Rightarrow $ $ {{[{\mu _{r}}A]} _{C}}+{{[{\mu _{r}}A]} _{F}}={{[{\mu _{v}}A]} _{C}}+{{[{\mu _{v}}A]} _{F}} $

$ = $

$ 1.5\times 19+6\times 1.66=38.5 $ Resultant $ \delta ={{[({\mu _{r}}-1)Al]} _{C}}+{{[({\mu _{r}}-1)A]} _{F}} $

$ = $

$ {{[{\mu _{r}}A]} _{C}}+{{[{\mu _{r}}A]} _{F}}-(A _{C}+A _{F}) $ = $ 38.5-(19+6)={{13.5}^{o}} $



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