A microscope is focused on a mark on a piece of paper. A slab of glass with a thickness of 3 cm and a refractive index of 1.5 is placed over the mark. How should the microscope be moved to bring the mark back into focus?

The microscope should be moved 1 cm closer to the glass slab to focus on the mark again. This is because the glass slab causes a refractive shift, calculated using the formula for apparent shift in a glass slab due to refraction, causing the image to appear 1 cm closer than it is.

Explanation:

The process covered in this scenario is known as refraction, which describes how light bends when it passes from one medium to another with a different refractive index. The refractive index of the glass slab is given as 1.5, and its thickness as 3 cm. For the microscope to focus on the mark again, it should be moved toward the slab by a distance equal to the apparent shift of the mark caused by placing the glass slab over it.

The formula for the apparent shift of light due to refraction in a glass slab is given by d = t (1-1/n), where 'd' is the apparent shift, 't' is the thickness of the slit, and 'n' is the refractive index. Plugging the given values, we get d = 3 cm (1 - 1/1.5), which gives d = 1 cm.

This means the microscope has to be moved 1 cm towards the glass slab to focus on the mark again. Thus, understanding refraction and the adjustments needed in microscopy can solve this problem.

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