Question

A transparent sphere of radius 20 cm and refractive index 1.6 is fixed in a hole of the partition separating the two media: A(refractive index $n_1$= 1.2 ) and B (refractive index $n_3$ =1.7). A luminous point object is placed 120 cm from surface of sphere in medium A. It is viewed from D in medium B in a direction normal to the sphere. Find the position of the image formed by the rays, from point N.

Answer 1

A ray starting from O,at first gets refracted from the surface M and forms an image at $I_1$

Using $\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$u=-120cm,R=20cm$

$\frac{1.6}{v_1}-\frac{1.2}{-120}=\frac{1.6-1.2}{20}$

$v_1=160cm$

Now the ray from $I_1$ gets refracted from the surface N anf forms an image at $I$.

So, $u=160-40=\pm 120cm,R=-20cm$

$\frac{n_3}{v}-\frac{n_2}{u}=\frac{n_3-n_2}{R}$

$v=204cm$

Thus the final image will from at $204cm$ right of N.