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}} $
