Question

There is an equiconvex glass lens with radius of each face as R and ${ } _ { a } \mu _ { g } = 3 / 2$and${ } _ { a } \mu _ { w } = 4 / 3$. If there is water in object space and air in image space, then the focal length is

• A. 2R
• B. R
• C. 3 *R/*2
• D. $R ^ { 2 }$

Answer 1

Answer: (C)

3 *R/*2

Answer 2

Consider the refraction of the first surface i.e. refraction from rarer medium to denser medium

$\frac { \left( \frac { 3 } { 2 } \right) - \left( \frac { 4 } { 3 } \right) } { R } = \frac { \frac { 4 } { 3 } } { \infty } + \frac { \frac { 3 } { 2 } } { v _ { 1 } } \Rightarrow v _ { 1 } = 9 R$

Now consider the refraction at the second surface of the lens i.e. refraction from denser medium to rarer medium

$\frac { 1 - \frac { 3 } { 2 } } { - R } = - \frac { \frac { 3 } { 2 } } { 9 R } + \frac { 1 } { v _ { 2 } } \Rightarrow v _ { 2 } = \left( \frac { 3 } { 2 } \right) R$

The image will be formed at a distance do $\frac { 3 } { 2 } R$. This is equal to the focal length of the lens.