Question

The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 Cm. Then the refractive index of the material of the lens is :

• A. $\frac { 3 } { 2 }$
• B. $\frac { 4 } { 3 }$
• C. $\frac { 9 } { 8 }$
• D. $\frac { 5 } { 3 }$

Answer 1

Answer: (A)

$\frac { 3 } { 2 }$

Answer 2

: Power of lens, P (in dioptre)

$= \frac { 100 } { \text { focallength } ( \text { Odl njb) } \mathrm { f } ( \text { in cm } ) }$

$\therefore \mathrm { f } = \frac { 100 } { 10 } = 10 \mathrm {~cm}$

According to lens maker’s formula

$\frac { 1 } { \mathrm { f } } = ( \mu - 1 ) \left( \frac { 1 } { \mathrm { R } _ { 1 } } - \frac { 1 } { \mathrm { R } _ { 2 } } \right)$

For biconvex lens,

$\frac { 1 } { \mathrm { f } } = ( \mu - 1 ) \left( \frac { 2 } { \mathrm { R } } \right) \Rightarrow \frac { 1 } { 10 } = ( \mu - 1 ) \left( \frac { 2 } { 10 } \right)$

$( \mu - 1 ) = \frac { 1 } { 2 } \Rightarrow \mu = \frac { 1 } { 2 } + 1 = \frac { 3 } { 2 }$