Question

A tank is filled with to a height of 15.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 8.5 cm. if water is replaced by a liquid of refractive index 1.94 upto the same height, by what distance would the microscope same height, by what distance would the microscope have to be moved to focus on the needle again?

• A. 1.00 cm
• B. 2.37 cm
• C. 0.52 cm
• D. 3.93 cm

Answer 1

Answer: (C)

0.52 cm

Answer 2

: Actual depth of the needle in water

$\mathrm { h } _ { 1 } = 15.5 \mathrm {~cm}$

Apparent depth of needle in water

$\mathrm { h } _ { 2 } = 8.5 \mathrm {~cm}$

$\therefore \mu _ { \text {water } } = \frac { \mathrm { h } _ { 1 } } { \mathrm {~h} _ { 2 } } = \frac { 15.5 } { 8.5 } = 1.82$

Hence, $\mu _ { \text {water } } = 1.82$ when water replaced by a liquid of refractive index $\mu ^ { \prime }$ = 1.94. The actual depth remains the same, but its apparent depth changes. Let H be the new apparent depth of the needle

$\therefore \mu ^ { \prime } = \frac { \mathrm { h } _ { 1 } } { \mathrm { H } }$ or $\mathrm { H } = \frac { \mathrm { h } _ { 1 } } { \mu ^ { \prime } } = \frac { 15.5 } { 1.9 } = 7.98 \mathrm {~cm}$

Here, H is less than Thus to focus the needle again, the microscope should be moved up. distance by which the microscope should be moved up

$= 8.5 - 7.98 = 0.52 \mathrm {~cm}$