Question

A Plano-convex lens is made of material of refractive index 1.6. The radius of curvature of the curved surface is 60cm. The focal length of the lens is:
A. 50cm
B. 100cm
C. 200cm
D. 400cm

Answer 1

Refractive index: Refractive index is a dimensionless number that describes how fast light travels through the material. Refractive index is denoted by ‘n’. As we know that
$\Rightarrow \eta = \dfrac{c}{v}$
$\eta = refractive index$
c=speed of light
v=phase velocity of light

Complete step by step solution:
Given,
Refractive index of material of lens,$\mu = 1.6$
Radius of curvature of plane surface${R_1} = \infty$
Radius of curvature of curved convex surface ${R_2} = - 60cm$
Using the lens maker formula:
$\Rightarrow \dfrac{1}{f} = (\mu - 1)(\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}})$
Put the value in that equation
$\Rightarrow \dfrac{1}{f} = (1.6 - 1)(\dfrac{1}{\infty } - \dfrac{1}{{ - 60}})$
$\Rightarrow \dfrac{1}{f} = (0.6)(\dfrac{1}{{60}})$
$\Rightarrow \dfrac{1}{f} = \dfrac{1}{{100}}$
The focal length of the lens are:
$\Rightarrow f = 100cm$
So the answer is (B)100cm.

Note: The radius of curvature of the plane surface of Plano-convex surface is always infinite and the image is real. Refractive index is a measure of how fast light travels through the medium. The highest the refractive index the slower the light passes. Refractive index depends on the electric and magnetic properties of the medium. Diamond has the highest refractive index.