A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness $3 ext{ cm}$ and

Question

A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness $3 	ext{ cm}$ and a refractive index $1.5$ is placed over the mark. How should the microscope be moved to get the mark in focus again?

Accepted Answer

1. **Identify the Phenomenon:** When a glass slab of thickness $t$ and refractive index $\mu$ is placed over an object, the object appears raised due to refraction. This is known as the normal shift.
2. **Formula for Normal Shift:** The shift $\Delta t$ is given by:
   $$ \Delta t = t \left( 1 - \frac{1}{\mu} ight) $$
3. **Calculation:** Given $t = 3 	ext{ cm}$ and $\mu = 1.5$.
   $$ \Delta t = 3 \left( 1 - \frac{1}{1.5} ight) $$
   $$ \Delta t = 3 \left( 1 - \frac{2}{3} ight) $$
   $$ \Delta t = 3 \left( \frac{1}{3} ight) = 1 	ext{ cm} $$
4. **Conclusion:** The image of the mark is raised by $1 	ext{ cm}$. To bring the image back into focus, the microscope must be moved upward by the same distance, i.e., $1 	ext{ cm}$.

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