Question

A point object is placed in front of a 5 cm thick plane glass mirror. Find the location of final image with respect to object.

• A. $\frac{35}{3}cm$
• B. 15 cm
• C. $\frac{40}{3}cm$
• D. $\frac{80}{3}cm$

Answer 1

The correct option is D $\frac{80}{3}cm$

Mirror can be shifted to new position C' D'. Distances are shown in the figure below.

Image distance from C' D' $=10+\frac{5}{3/2}=10+\frac{10}{3}$
$=\frac{40}{3}cm$
Separation between object and image is $=\frac{80}{3}cm$

Alternate solution:
The polished mirror face CD shifts to apparent depth as face C'D'.
Apparent depth $=\frac{Realdepth}{Refractiveindex}=\frac{5}{\mu }=\frac{5\times 2}{3}$
Thus, distance of object from shifted mirror face
$=10+\frac{10}{3}=\frac{40}{3}cm$
Distance between object and image
$=\frac{40}{3}+\frac{40}{3}=\frac{80}{3}cm$
(Image is as behind the plane mirror as object in front of it.)

Hence, the correct answer is option (d).

Why this question? Concept: The distance of image from the apparent position of plane mirror is same as the distance of object from the apparent position of plane mirror.