Optics Question 816
Question: A plastic hemisphere has a radius of curvature of 8 cm and an index of refraction of 1.6. On the axis halfway between the plane surface and the spherical one (4 cm from each) is a small object 0. The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately
Options:
A) 1.0 cm
B) 1.5 cm
C) 3.75 cm
D) 2.5 cm
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Distance of image from the plane surface is as follows:
$ x _{1}=\frac{4}{1.6}=2.5cm( d _{app}=\frac{d _{actual}}{\mu } ) $
For the curved side $ \frac{1.6}{4}+\frac{1}{x _{2}}=\frac{1-1.6}{8} $
$ \therefore x _{2}\approx -3.0cm $ The minus sign means the image is on the object side.
