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)
/A dancer medinim of refractive indey 15 has a
4​

Answer 1

answer : option (3) 24cm from the centre

explanation : Let object is located at point A. refraction at A produces a virtual image at I' and this I' behaves as virtual object for surface B and form final real image at I.

refraction at A,

using formula, $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

⇒1.5/v' - 1/-36 = (1.5 - 1)/12

⇒1.5/v' + 1/36 = 1/24

⇒1.5/v' = 1/24 - 1/36 = 1/72

⇒1/v' = 1/108

⇒v' = 108cm

now, u = -108cm

again, using formula, $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

⇒1/v - 1.5/-108 = (1 -1.5)/-12

⇒1/v + 1/72 = 1/24

⇒1/v = 1/24 - 1/72 = 1/36

hence, v = 36cm from the surface and 24cm from the centre.

hence, option (3) is correct.

Answer 2

Answer:

(4) Both (1) and (2)

Solution in above photo....;)