Question

A bioconvex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.24$. Both the curved surfaces are of the same radius of curvture $R=14\text{cm}$ . For this, biconvex lens, when an object distance of $40\text{cm}$, the image distance will be:

• A. $-28.0\text{cm}$
• B. $-40.0\text{cm}$
• C. $-21.5\text{cm}$
• D. $-13.3\text{cm}$

Answer 1

The correct option is B $-40.0\text{cm}$

Effective focal length of combination is $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
$\frac{1}{f}=\left(\frac{{\mu }_1-1}{R_1}\right)+\left(\frac{{\mu }_2-1}{R_2}\right)\Rightarrow \frac{1}{f}=\frac{0.5}{14}+\frac{0.2}{14}$
$f=20\text{cm}$
Using lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}-\frac{1}{-40}=\frac{1}{20}v=40\text{cm}$