Question

Flint glass prism is joined by a crown glass prism to produce dispersion without deviation. The angle of prism of these two glasses are $6^{\circ }$ and $8^{\circ }$ respectively. The refractive index of flint glass for yellow ray is $1.7$. The referactive index of crown glass prism for yellow ray will be :

• A. $1.2$
• B. $1.45$
• C. $1.5$
• D. $1.75$

Answer 1

The correct option is C $1.5$

We know that, for dispersion without deviation :
${\delta }_1+{\delta }_2=0$
$\Rightarrow A(\mu -1)+A^{\prime }({\mu }^{\prime }-1)=0$, where $A$ is the angle of flint glass prism and $A^{{}^{\prime }}$ is the angle of crown glass prism.
Also, $\mu$ and ${\mu }^{{}^{\prime }}$ are refractive indices of flint glass prism and crown glass prism respectively for yellow ray.
$\Rightarrow {\mu }^{\prime }=-\frac{A}{A^{\prime }}(\mu -1)+1$
From the data given in the question,
$\Rightarrow {\mu }^{\prime }=-\left(\frac{6}{-8}\right)(1.7-1)+1$
$(\because$ one of the prism is inverted so it's angle is considered to be negative$)$
$\Rightarrow {\mu }^{\prime }=0.52+1$
Or, ${\mu }^{\prime }=1.52\approx 1.5$

Hence, option $\left(c\right)$ is the correct answer.