Question

Flint glass prism is joined by a crown glass prism to produce dispersion without deviation. The refractive indices of these prisms for yellow ray are $1.602$ and $1.500$ respectively. If the angle of flint glass prism is ${10}^{\circ }$. Then the angle of crown glass prism will be :

• A. ${12.04}^{\circ }$
• B. ${11.50}^{\circ }$
• C. ${13.25}^{\circ }$
• D. ${20}^{\circ }$

Answer 1

The correct option is A ${12.04}^{\circ }$

We know that, for dispersion without deviation :

${\delta }_1+{\delta }_2=0$

$\Rightarrow A(\mu -1)+A^{\prime }({\mu }^{\prime }-1)=0$

Here, $A$ 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.
$\Rightarrow A^{\prime }=-A\left(\frac{\mu -1}{{\mu }^{\prime }-1}\right)$

From the data given in the question,
$A^{\prime }=-{10}^{\circ }\left(\frac{1.602-1}{1.500-1}\right)$

$\Rightarrow A^{\prime }=-{10}^{\circ }\times \frac{0.602}{0.500}$

$\Rightarrow A^{\prime }=-{10}^{\circ }\times 1.204$

Or, $A^{\prime }=-{12.04}^{\circ }$

Here negative sign indicates that prism is inverted.

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