Question

The dispersive powers of flint glass and crown glass are $0.053$ and $0.034$ respectively and their mean refractive indices are $1.68$ and $1.53$ for white light. Calculate the angle of the flint glass prism required to form an achromatic combination with a crown glass prism of refracting angle $4°.$

• A. $2^{\circ }$
• B. $4^{\circ }$
• C. $5^{\circ }$
• D. $6^{\circ }$

Answer 1

Answer: (C)

Given-Glass type	Flint	Crown
Dispersive power	$0.053$	$0.034$
Refractive Index of Mean Colour	$1.68$	$1.53$
Refracting Angle	$?$	$4^{\circ }$

Condition for Achromatism $=\frac{{\omega }_1}{{\omega }_1}=\frac{f_1}{f_2}$
$\Rightarrow \frac{{\left(\omega \right)}_1}{{\left(\omega \right)}_2}=\frac{\left({\left(\mu \right)}_1-1\right)A_1}{\left({\left(\mu \right)}_2-1\right)A_2}$
$\Rightarrow \frac{0.053}{0.034}=\frac{\left(1.68-1\right)\cdot A}{\left(1.53-1\right)\cdot 4}$
$\Rightarrow \frac{0.053}{0.034}=\frac{\mathrm{0.68.}A}{0.53\times 4}$
$A=4.85\approx 5$