Question

What is the refractive index of material of a plano – convex lens, if the radius of curvature of the convex surface is 10 cm and focal length of the lens is 30 cm?

• A. $\frac { 6 } { 7 }$
• B. $\frac { 7 } { 4 }$
• C. $\frac { 2 } { 3 }$
• D. $\frac { 4 } { 3 }$

Answer 1

Answer: (D)

$\frac { 4 } { 3 }$

Answer 2

: According to lens maker’s formula

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

Here, $\mathrm { f } = 30 \mathrm {~cm} , \mathrm { R } _ { 1 } = \infty$ (For plane surface)

$\therefore \frac { 1 } { 30 } = ( \mu - 1 ) \left( \frac { 1 } { \infty } - \frac { 1 } { - 10 } \right) \Rightarrow \frac { 1 } { 30 } = \frac { ( \mu - 1 ) } { 10 }$

$3 ( \mu - 1 ) = 1$

$3 \mu = 4$

$\mu = \frac { 4 } { 3 }$