Question

A microscope is focused on an ink mark on the top of a table. If we place a glass slab of 3 cm thick on it, how should the microscope be moved to focus the ink spot again? The refractive index of glass is 1.5.
A. 2 cm upwards
B. 2 cm downwards
C. 1 cm upwards
D. 1 cm downward

Answer 1

Hint: Use the relation between apparent depth and real depth of the image in the medium of refractive index\[\mu \]. Subtract the depth of the ink mark you obtained from the real depth to get the final answer.

Formula used:
\[{\text{Apparent}}\,\,{\text{depth}} = \dfrac{{{\text{Real depth}}}}{\mu }\]
Here, \[\mu \] is the refractive index.

Complete step by step answer:
We know that when a light ray passes through denser medium to rare medium, the ray of light bends away from the normal. Due to the bending of light rays away from the normal, the image of the object appears to be shifted upward.
We have the formula for apparent depth of the object as seen through a medium of refractive index \[\mu \] is,
\[{\text{Apparent}}\,\,{\text{depth}} = \dfrac{{{\text{Real depth}}}}{\mu }\]
We have given that the real depth of the ink mark is the thickness of the glass placed above it. Also, the refractive index of the glass is 1.5.
Therefore, we can calculate the apparent depth of the image of the ink mark by substituting 3 cm for real depth and 1.5 for \[\mu \] in the above equation.
\[{\text{Apparent}}\,\,{\text{depth}} = \dfrac{{\text{3}}}{{1.5}}\,cm\]
\[ \Rightarrow {\text{Apparent}}\,\,{\text{depth}} = 2\,cm\]
Therefore, we can see the image of the ink mark appears to be raised by the distance\[3\,cm - 2\,cm = 1\,cm\].
Thus, to focus the ink mark, the microscope has to be shifted upward by the distance 1 cm.

So, the correct answer is “Option C”.

Note:
Students may incorrectly answer this question as 2 cm upward as the depth of the image in the second case is 2 cm. But note that, 2 cm is the depth of the ink mark as seen from the above. Therefore, the image is formed 1 cm above the base of the glass slab.