Question

In the figure, light is incident on a thin lens from the left as shown. The radius of curvature for both the surfaces is $R$. Determine the focal length of this system.

• A. None of these
• B. $\frac{{\mu }_{3}R}{{\mu }_3-{\mu }_1}$
• C. $\frac{{\mu }_{2}R}{{\mu }_3-{\mu }_1}$
• D. $\frac{{\mu }_{1}R}{{\mu }_3-{\mu }_1}$

Answer 1

The correct option is B $\frac{{\mu }_{3}R}{{\mu }_3-{\mu }_1}$

For refraction at the first surface,

$\frac{{\mu }_2}{v_1}-\frac{{\mu }_1}{\infty }=\frac{{\mu }_2-{\mu }_1}{+R}.....\left(1\right)$

For refraction at second surface,

$\frac{{\mu }_3}{v_2}-\frac{{\mu }_2}{v_1}=\frac{{\mu }_3-{\mu }_2}{+R}.....\left(2\right)$

On adding $\left(1\right)$ and $\left(2\right)$,

$\frac{{\mu }_3}{v_2}=\frac{{\mu }_3-{\mu }_1}{R}$

$\Rightarrow v_2=\frac{{\mu }_{3}R}{{\mu }_3-{\mu }_1}=f$

[since incident rays are parallel, final image is formed at the focus of the system.]