Optics Question 680
Question: A point object is placed at the center of a glass sphere of radius 6 cm and refractive index 1.5. The distance of the virtual image from the surface of the sphere is
[IIT-JEE (Screening) 2004]
Options:
A) 2 cm
B) 4 cm
C) 6 cm
D) 12 cm
Show Answer
Answer:
Correct Answer: C
Solution:
Using refraction formula $ \frac{ _{1}{\mu _{2}}-1}{R}=\frac{ _{1}{\mu _{2}}}{v}-\frac{1}{u} $ in given case, medium (1) is glass and (2) is air .
So $ \frac{ _{g}{\mu _{a}}-1}{R}=\frac{ _{g}{\mu _{a}}}{v}-\frac{1}{u} $
$ \Rightarrow \frac{\frac{1}{1.5}-1}{-6}=\frac{1}{1.5v}-\frac{1}{-6} $
$ \Rightarrow \frac{1-1.5}{-6}=\frac{1}{v}+\frac{1.5}{6} $
$ \Rightarrow \frac{0.5}{6}=\frac{1}{v}+\frac{1}{4} $
$ \Rightarrow \frac{1}{v}=\frac{1}{12}-\frac{1}{4}=-\frac{2}{12}=-\frac{1}{6} $
Therefore v = 6 cm
