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A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again :-
A
1 cm upward
B
4.5 cm downward
C
1 cm downward
D
2 cm upward
Detailed Solution
When a glass slab is placed over the mark, the mark appears raised because of refraction.
Apparent depth $= \dfrac{t}{\mu} = \dfrac{3}{1.5} = 2$ cm
Upward shift of the mark (normal shift) $= t\left(1 - \dfrac{1}{\mu}\right)$
$= 3\left(1 - \dfrac{1}{1.5}\right) = 3 \times \dfrac{1}{3}$
$= 1$ cm
The image of the mark is 1 cm closer to the microscope, so the microscope must be moved 1 cm upward to bring the mark into focus again.
Apparent depth $= \dfrac{t}{\mu} = \dfrac{3}{1.5} = 2$ cm
Upward shift of the mark (normal shift) $= t\left(1 - \dfrac{1}{\mu}\right)$
$= 3\left(1 - \dfrac{1}{1.5}\right) = 3 \times \dfrac{1}{3}$
$= 1$ cm
The image of the mark is 1 cm closer to the microscope, so the microscope must be moved 1 cm upward to bring the mark into focus again.