Question

A point object is situated at a distance of $36$ cm from the centre of the sphere of radius $12$ cm and refractive index $1.5$. Locate the position of the image due to refraction through sphere.

• A. $24$ cm from the surface
• B. $36$ cm from the centre
• C. $24$ cm from the centre
• D. Both (1) & (2)

Answer 1

The correct option is C $24$ cm from the centre

We are given that

Distance of point object, $u=-36cm$

Radius of of curvature, $12cm$

Refractive index, $\mu =1.5$

We have to find the position of image due to refraction through sphere.

Let point object is located at point $A$. Refraction through surface $A$ produces virtual image I.Then virtual image $I$ acts as object for surface $B$. Then , surface $B$ produce final real image $I^{\prime }$ of point object.

We know that lens maker formula

$\frac{\mu }{v_1}=\frac{1}{u}=\frac{\mu -1}{R}$

Substituting the value, then we get

$\frac{1.5}{v_1}-\frac{1}{-36}=\frac{1.5-1}{12}$

$\frac{1.5}{v_1}=\frac{1}{24}-\frac{1}{36}$

$\frac{1.5}{v_1}=\frac{3-2}{7.2}=-\frac{1}{72}$

$v_1=-1.5\times 72$

$v_1=-108cm$

Now, $v_1$ acts as object for surface $B$

Then, again using lens maker formula,

$\frac{1}{v_2}-\frac{1.5}{-108}=\frac{1-1.5}{-12}$

$\frac{1}{v_2}=\frac{1}{24}-\frac{1}{72}$

$v_2=\frac{3-2}{72}=\frac{2}{72}=36cm$

Hence, $36cm$ from the surface and $24cm$ from the center of sphere because ardius is $12cm$

So correct answer is option (C).