Question

Two glass prisms $P_1$ and $P_2$ are to be combined together to produce dispersion without deviation. The angles of the prisms $P_1$ and $P_2$ are selected as $4^{\circ }$ and $3^{\circ }$ respectively. If the refractive index of prism $P_1$ is $1.54$, then that of $P_2$ will be

• A. 1.48
• B. 1.58
• C. 1.62
• D. 1.72

Answer 1

Answer: (D)

Given for prism $P_1$
$\mu =1.54,A=4^{\circ }$
For prism $P_2$
${\mu }^{\prime }=?,A^{\prime }=3^{\circ }$
For no deviation $=\delta +{\delta }^{\prime }=0$
$\Rightarrow (\mu -1)A=\left({\mu }^{\prime }-1\right)A^{\prime }$
$\Rightarrow (1.54-1)4=\left({\mu }^{\prime }-1\right)3$
On solving we get ${\mu }^{\prime }=1.72$