Question

A convex refracting surface has a radius of 12 cm. Light is incident in air (n = 1) and refracted into a medium with an index of refraction of 1.5. Light incident parallel to the central axis is focused at a point _____________

Answer 1

Answer:

36cm from the surface

Explanation:

Equation of refraction of a lens is expression according to the formula given below;

$\dfrac{n_2}{v} = \dfrac{n_1}{u}= \dfrac{n_2-n_1}{R}$

R is the radius of curvature of the convex refracting surface = 12cm

v is the image distance from the refracting surface

u  is the object distance from the refracting surface

n₁ and n₂ are the refractive indices of air and the medium respectively

Given parameters

R = 12 cm

u = $\infty$ (since light incident is parallel to the axis)

n₁  = 1

n₂  = 1.5

Required

focus point of the light that is incident and parallel to the central axis (v)

Substituting this values into the given formula we will have;

$\dfrac{1.5}{v} - \dfrac{1}{\infty}= \dfrac{1.5-1}{12}\\\\\dfrac{1.5}{v} -0= \dfrac{0.5}{12}\\\\\dfrac{1.5}{v}= \dfrac{0.5}{12}$

Cross multiply

$1.5*12 = 0.5*v\\ \\18 = 0.5v\\\\v = \frac{18}{0.5}\\ \\v = 36cm$

Hence  Light incident parallel to the central axis is focused at a point 36cm from the surface