Question

A biconvex thin lens is prepared from glass $(\mu =1.5)$, the two bounding surfaces having equal radii of 25 cm each. One of the surfaces is silvered from outside to make it reflecting. Where should an object be placed before this lens so that the image is formed on the object itself?

• A. -10 cm
• B. -12 cm
• C. - 12.5 cm
• D. - 14 cm

Answer 1

The correct option is C

- 12.5 cm

Refer to figure (18-W21). The object is placed at O. A ray OA starting from O gets refracted into the glass at the first surface and hits the silvered surface along AB. To get the image at the object, the rays should retrace their path after reflection from the silvered surface. This will happen only if AB falls normally on the silvered surface. Thus, AB should appear to come from the centre $C_2$ of the second surface. Thus, due to the refraction at the first surface, a virtual image of O is formed at $C_2$.
For this case,
$v=P{C}_2=-25cm,R=P{C}_1=+25cm,{\mu }_1=1,{\mu }_2=1.5$.
We have,
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$
or, $\frac{1.5}{-25cm}-\frac{1}{u}=\frac{1.5-1}{25cm}$
or, $\frac{1}{u}=\frac{1.5}{25cm}-\frac{0.5}{25cm}$
or, $u=-12.5cm$
Thus, the object should be placed at a distance of 12.5 cm from the lens.