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# A prism of crown glass refracting angle of $50^{\circ}$ and mean refractive index $=1.51$ is combined with one flint glass prism of refractive index $=1.65$ to produce no deviation Then the angle of flint glass is

$(a)\;3.92 ^{\circ} \\ (b)\;1.49^{\circ} \\ (c)\;2.67 ^{\circ} \\ (d)\;6.28^{\circ}$

Let $A'$ be angle of flit glass prism.
Here $A=5^{\circ}$ and $\mu= 1.51$ for crown glass prism
$\delta =( \mu -1)A=(1.51-1) \times 5 =2.55$
Deviation produced by flint glass
$\delta =(\mu'-1)A'= (1.65-1) A'$
$\qquad= 0.65\;A'$
For no deviation $\delta'=\delta$
$0.65 A'= 2.55$
$A'= \large\frac{2.55}{0.65}$
$\qquad= 3.92^{\circ}$
Hence a is the correct answer.

edited Jul 21, 2014