question_answer

A concave mirror is placed at the bottom of an empty tank with face upwards and axis vertical.  When sunlight falls normally on the mirror, it is focussed at distance of 32 cm from the mirror.  If the tank filled with water \[\left( \mu =\frac{4}{3} \right)\] upto a height of 20 cm, then the sunlight will now get focussed at [UPSEAT 2002]

A)            16 cm above water level 

B)            9 cm above water level

C)            24 cm below water level 

D)            9 cm below water level

Correct Answer: B

Solution :

                   Sun is at infinity i.e. \[u=\infty \] so from mirror formula we have \[\frac{1}{f}=\frac{1}{-32}+\frac{1}{(-\infty )}\Rightarrow f=-32\]\[cm\].                    When water is filled in the tank upto a height of 20 cm, the image formed by the mirror will act as virtual object for water surface. Which will form it?s image at \[I\] such that \[\frac{\text{Actual height}}{\text{Apperant height}}=\frac{{{\mu }_{w}}}{{{\mu }_{a}}}\] i.e. \[\frac{BO}{BI}=\frac{4/3}{1}\]                    \[\Rightarrow \] \[BI=BO\times \frac{3}{4}\]=\[12\times \frac{3}{4}=\]\[9\]\[cm\].