Q. 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 $4°.$
NTA AbhyasNTA Abhyas 2022
Solution:
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 $=\frac{\omega _{1}}{\omega _{1}}=\frac{f_{1}}{f_{2}}$
$\Rightarrow \, \, \frac{\left(\omega \right)_{1}}{\left(\omega \right)_{2}}=\frac{\left(\left(\mu \right)_{1} - 1\right) A_{1}}{\left(\left(\mu \right)_{2} - 1\right) A_{2}}$
$\Rightarrow \, \, \frac{0.053}{0.034}=\frac{\left(1.68 - 1\right) \cdot A}{\left(1.53 - 1\right) \cdot 4}$
$\Rightarrow \, \, \frac{0.053}{0.034}=\frac{0.68 . A}{0.53 \times 4}$
$A=4.85\approx5$
| Given-Glass type | Flint | Crown |
| Dispersive power | $0.053$ | $0.034$ |
| Refractive Index of Mean Colour | $1.68$ | $1.53$ |
| Refracting Angle | $?$ | $4^\circ $ |