Question

Two identical plano-convex lenses $L_1({\mu }_1=1.4)$ and $L_2({\mu }_2=1.5)$ of radii of curvature $R=20cm$ are placed as shown in fig. Find the position of the image of the parallel beam of light relative to the common principal axis.

• A. $14.3cm$
• B. $22.2cm$
• C. $31.2cm$
• D. $21.8cm$

Answer 1

The correct option is B $22.2cm$

Refraction occurs at three surfaces.

Consider refraction at first surface,

$\frac{1.4}{v_1}-\frac{1}{-\infty }=\frac{1.4-1}{+20}$

Consider refraction from second surface,

$\frac{1.5}{v_2}-\frac{1.4}{v_1}=\frac{1.5-1.4}{\infty }$

Consider refraction from third surface,

$\frac{1}{v_3}-\frac{1.5}{v_2}=\frac{1-1.5}{-20}$

Adding the three equations gives,

$\frac{1}{v_3}=\frac{1.4-1}{+20}+\frac{1.5-1.4}{\infty }+\frac{1-1.5}{-20}$

Therefore, $v_3=\frac{200}{9}cm=22.2cm$