Question

What is the refractive index of the material of a plano convex lens, if the radius of the curvature of the convex surface is $10cm$ and the focal length of the lens is $30cm$ ?
A. $\dfrac{6}{3}$
B. $\dfrac{7}{4}$
C. $\dfrac{2}{3}$
D. $\dfrac{4}{3}$

Answer 1

Hint: You can calculate the lens maker formula, i.e. $\dfrac{1}{f} = \left( {\mu - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right)$. Here, keep the ${R_1} = \infty $ , ${R_2} = - 10cm$ and $f = 30cm$ to calculate the value of the refractive index of the lens.

Complete answer:
For this solution, we will have to use the lens maker formula, the lens maker formula is used to design different lenses according to the user’s demand with different focus length, the radius of curvature of both the faces of the lens and the refractive index of the material that the lens is made up of.
We know that the lens maker’s formula is
$\dfrac{1}{f} = \left( {\mu - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right)$
Here, $f = $ The focal length of the plano convex lens
$\mu = $ The refractive index of the material used to make the plano convex lens
${R_1} = $ The radius of curvature of one face of the lens
${R_2} = $ The radius of curvature of the second face of the lens
In the problem, we are given $f = 30cm$
${R_1} = \infty $ (because one side of the plano convex is plane, hence the focus will lie at infinity)
${R_2} = - 10cm$ (the radius of curvature of the curved side of the plano convex lens)
So, for this problem the lens maker’s formula is
$\dfrac{1}{{30}} = \left( {\mu - 1} \right)\left( {\dfrac{1}{\infty } - \dfrac{1}{{ - 10}}} \right)$
$\dfrac{1}{{30}} = \left( {\mu - 1} \right)\left( {\dfrac{1}{{10}}} \right)$
$\mu = \dfrac{4}{3}$

So, the correct answer is “Option D”.

Note:
The refractive index of a material is the ratio of the angle of incidence to the angle of refraction. We know that every material has its unique refractive index, this is because the speed of light is different in every medium, and thus light bends when it travels from one medium to the other.