Optics Question 945
Question: A vertical microscope is focused on a point at the bottom of an empty tank. Water $ ( \mu =\frac{4}{3} ) $ is then poured into the tank. The height of the water column is 4 cm. Another lighter liquid, which does not mix with water and which has refractive index $ \frac{3}{2} $ is then poured over the water. The height of liquid column is 2 cm. What is the vertical distance through which the microscope must be moved to bring the object in focus again?
Options:
A) 2.61 m
B) 1.55 m
C) 3.12 m
D) 1.67 m
Show Answer
Answer:
Correct Answer: D
Solution:
[d] The apparent shift of the bottom point upwards will be
$ x=x _{1}+x _{2} $
$ =t _{1}( 1-\frac{1}{{\mu _{1}}} )+t _{2}( 1-\frac{1}{{\mu _{2}}} ) $
$ =4( 1-\frac{1}{4/3} )+2( 1-\frac{1}{3/2} ) $
$ =4( 1-\frac{3}{4} )+2( 1-\frac{2}{3} )=1.67cm $
