Question

A convex lens of focal length 0.2 m and made of glass is immersed in water $\left( { } ^ { \mathrm { a } } \mu _ { \mathrm { w } } = 1.33 \right)$ .Find the change in the focal length of the lens:

• A. 5.8 m
• B. 0.58 Cm
• C. 0.58 m
• D. 5.8 cm

Answer 1

Answer: (C)

0.58 m

Answer 2

: Using $\frac { 1 } { \mathrm { f } _ { \mathrm { a } } } = \left( { } ^ { \mathrm { a } } \mu _ { \mathrm { g } } \right) \left( \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right)$

Here, $\mathrm { f } _ { \mathrm { a } } = 0.2 \mathrm {~m} , { } ^ { \mathrm { a } } \mu _ { \mathrm { g } } = 1.50$

$\therefore \frac { 1 } { 0.2 } = ( 1.50 - 1 ) \left( \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right) = 0.50 \left( \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right)$

$\Rightarrow \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } = 10$

Consider be the focal length of the lens, when immersed in water if be refractive index of glass w.r.t. water, then

Now,

Hence, change in focal length of the lens,