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 $1.5$.

Answer 1

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:

1. Here, the thickness of the glass slab = Real depth
2. Hence, apparent depth = Real depth / Refractive index
3. Putting the given values, we get
4. Apparent depth = $\frac{3}{1.5}=2cm$
5. 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.