Question

A thin prism of angle $6^{\circ }$ made of glass of refractive index $1.5$ is combined with another thin prism made of glass of refractive index $1.75$ to produce dispersion without deviation. The angle of the second prism is :

• A. $7^{\circ }$
• B. $4^{\circ }$
• C. $9^{\circ }$
• D. $5^{\circ }$

Answer 1

The correct option is B $4^{\circ }$

Let deviation produced by first prism is $\delta$ and by second prism is ${\delta }^{\prime }$

For dispersion without deviation :
$\delta +{\delta }^{\prime }=0$
$\Rightarrow A(\mu -1)+A^{\prime }({\mu }^{\prime }-1)=0$

Here, $A=6^{\circ },\mu =1.5$, ${\mu }^{\prime }=1.75$ and $A^{\prime }$ is to be determined.

From the given data :
$6(1.5-1)+A^{\prime }(1.75-1)=0$
or, $3+A^{\prime }\left(\frac{3}{4}\right)=0$
$\Rightarrow A^{\prime }=-4^{\circ }$

Here, negative sign indicates that second prism is inverted with respect to first prism.

Why this question? Tip: For dispersion without deviation, $\delta +{\delta }^{\prime }=0$ and in order to satisfy this condition, the angle of one prism comes out to be -ve. This indicates that one prism is inverted.