Question

# A microscope is focused on an ink mark on the top of a table. If we place a glass slab $3cm$ thick on it, how should the microscope be moved to focus on the ink spot again? The refractive index of the glass slab is $1.5$.

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Solution

## Step 1. Given data:Thickness of glass slab = $3cm$ Refractive index of the glass slab = $1.5$Step 2. Formula used:Refractive index $\left(n\right)$ = $\frac{\mathrm{Real}\mathrm{depth}\left(\mathrm{D}\right)}{\mathrm{Apparent}\mathrm{depth}\left(\mathrm{d}\right)}$ Step 3. Calculations:Here, the thickness of the glass slab = Real depthHence, apparent depth = Real depth / Refractive indexPutting the given values, we getApparent depth = $\frac{3}{1.5}=2cm$Distance through which the microscope will be moved = Real depth - Apparent depth = $3-2=1cm$( upwards)Thus, the microscope should be moved $1cm$ in an upwards direction.

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