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

Question

Dr. Abubacker · Accepted Answer

(d) For achromatic combination $\omega_{C} = - \omega_{F}$
$\left\lbrack \left( \mu_{v} - \mu_{r} ight)A ightbrack_{C} = - \left\lbrack \left( \mu_{v} - \mu_{r} ight)A ightbrack_{F}$
$\Rightarrow \left\lbrack \mu_{r}A ightbrack_{C} + \lbrack\mu_{r}{Abrack}_{F} = \left\lbrack \mu_{v}A ightbrack_{C} + \left\lbrack \mu_{c}A ightbrack_{F}$
$= 1.5 	imes 19 + 6 	imes 1.66 = 38.5$
Resultant $\delta = \left\lbrack \left( \mu_{r} - 1 ight)A ightbrack_{C} + \left\lbrack \left( \mu_{r} - 1 ight)A ightbrack_{F}$
$= \left\lbrack \mu_{r}A ightbrack_{C} + \left\lbrack \mu_{r}A ightbrack_{F} - \left( A_{C} + A_{F} ight) = 38.5 - (19 + 6) = 13.5{^\circ}$

Q. An achromatic prism is made by crown glass prism $(A_{c} = 19{^\circ})$ and flint glass prism $(A_{F} = 6{^\circ})$. If $\ ^{C}\mu_{v} = 1.5$ and$\ ^{F}\mu_{v} = 1.66$, then resultant deviation for red coloured ray will be

Explanation

Reviewed by Dr. Abubacker

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