Question

14. 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.
(1) 24 cm from the surface
(2) 36 cm from the centre
(3) 24 cm from the centre
(4) Both (1) & (2)​

Answer 1

Answer:

4-both 1& 2..........

Answer 2

Answer:

3)24 cm from the center.

Explanation:

We are given that

Distance of point object=u=-36 cm

Radius of of curvature=12 cm

Refractive index=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' of point object.

We know that lens maker formula

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

Substitute the values then we get

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

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

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

$v_1=-1.5\times 72$

$v_1=-108 cm$

Now, $v_1$ acts as object for surface B

Then, again using lens maker formula

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

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

$v2=\frac{3-1}{72}=\frac{2}{72}$

$v_2=36 cm$

Hence, 36 cm from the surface and 24 cm from the center of sphere because radius is 12 cm.

Option 3 is true.