Question

A microscope is focussed on a coin lying at the bottom of a beaker. The microscope is now raised by 1 cm. To what depth should water be poured into the beaker so that the coin is again in focus? (The refractive index of water is $\frac{4}{3}$).

• A. 1 cm
• B. $\frac{4}{3}cm$
• C. 3 cm
• D. 4 cm

Answer 1

The correct option is D 4 cm

Suppose that real depth of water poured into the beaker be h and the microscope is raised upon to 1 cm to focus the coin placed in the beaker. Thus, the apparent depth of the coin becomes h’ = h -1
Now, the refractive index in terms of real and apparent depth is given as
$n=\frac{realdepth}{apparentdepth}$
$n=\frac{h}{h^{\prime }}$
$n=\frac{h}{h-1}$
$nh-n=h$
$nh-h=n$
$h=\frac{n}{n-1}$
On substituting the values in the above equation we get,
$h=\frac{\frac{4}{3}}{\frac{4}{3}-1}$
$h=\frac{\frac{4}{3}}{\frac{1}{3}}$
$h=\frac{4}{3}\times \frac{1}{3}$
$h=4cm$