Question

A plano-convex lens of refractive index ${\mu }_1$ and focal length $f_1$ is placed in contact with a plano-concave lens of refractive index ${\mu }_2$ and focal length $f_2$ as shown in figure. If the radius of curvature of each lens is $R$ and $|f_1|=2|f_2|$, then ${\mu }_1$ and ${\mu }_2$ are related as-

• A. $3{\mu }_2-2{\mu }_1=1$
• B. ${\mu }_1+{\mu }_2=3$
• C. $2{\mu }_1-{\mu }_2=1$
• D. $2{\mu }_2-{\mu }_1=1$

Answer 1

The correct option is C $2{\mu }_1-{\mu }_2=1$


Using lens makers' formula
Focal length of plano-convex lens using lens maker formula,
$R_1=\infty$ and $R_2=-R$
$$f_1=\frac{R}{{\mu }_1-1}$$

Focal length of plano-concave lens using lens maker formula,
$R_1=\infty$ and $R_2=R$
$$f_2=-\frac{R}{{\mu }_2-1}$$
Given, $|f_1|=2|f_2|$

$\Rightarrow \frac{R}{{\mu }_1-1}=2\times \frac{R}{{\mu }_2-1}$
$\Rightarrow 2{\mu }_1-2={\mu }_2-1$
$\Rightarrow 2{\mu }_1-{\mu }_2=1$
Hence, option (c) is the correct answer.