(A) For a direct vision spectroscope,the net deviation produced by the combination of prisms must be zero.Let $A_c = 9^o$ be the angle of the crown gl

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(A) For a direct vision spectroscope,the net deviation produced by the combination of prisms must be zero.Let $A_c = 9^o$ be the angle of the crown glass prisms and $A_f$ be the angle of the flint glass prisms.The refractive indices are $\mu_c = 1.53$ and $\mu_f = 1.60$.The total deviation $\delta_{net} = 3 \times \delta_c - 2 \times \delta_f = 0$.Substituting the formula for deviation $\delta = (\mu - 1)A$:$3(\mu_c - 1)A_c - 2(\mu_f - 1)A_f = 0$.$3(1.53 - 1) \times 9^o = 2(1.60 - 1) \times A_f$.$3(0.53) \times 9^o = 2(0.60) \times A_f$.$14.31^o = 1.2 \times A_f$.$A_f = \frac{14.31}{1.2} = 11.925^o \approx 11.9^o$.

Class 12 Physics Ray Optics and Optical Instruments Refraction Through Prism

Medium

Three prisms of crown glass,each having a prism angle of $9^o$,and two prisms of flint glass are used to make a direct vision spectroscope. What will be the angle of the flint glass prisms in degrees if the refractive index $\mu$ for flint glass is $1.60$ and $\mu$ for crown glass is $1.53$ (in $^o$)?

A
$11.9$
B
$16$
C
$15.3$
D
$9.11$

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Refraction Through Prism

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