Question

A concave mirror is placed inside water with its shining surface upward and principal axis vertical as shown in the figure. The final position of the image from the interface seen by an observer above interface if incident ray strikes normal to interface will be

• A. $7.5\text{cm}$ below the interface
• B. $7.5\text{cm}$ above the interface
• C. $9.5\text{cm}$ below the interface
• D. $9.5\text{cm}$ above the interface

Answer 1

The correct option is A $7.5\text{cm}$ below the interface

Since, the incident ray are striking normal to the surface, it will pass un-deviated through water and will strike the mirror parallel to its principal axis.
$\therefore$ object will be at $\infty$ for the mirror, its image will form at focus $(F=20\text{cm})$ from pole of mirror.
The reflected rays will once again suffer refraction at the interface, and they will bend away from normal. Thus, image position gets shifted above for the observer in air.


The real depth for the image $\left(I\right)$ is,
$P^{\prime }I=30-20=10\text{cm}$
On applying,
$\frac{{\mu }_{water}}{{\mu }_{air}}=\frac{\text{Real depth}}{\text{Apparent depth}}$
$\Rightarrow d_{app}=\frac{1\times 10}{\frac{4}{3}}$
$\therefore d_{app}=7.5\text{cm}$
Thus, final image is $7.5\text{cm}$ below the interface.

Why this question? It intends to test your ability to link the concepts of reflection and refraction in order to arrive at final conclusion.