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(C) For water, real depth $= 12 \,cm$. Apparent depth $= 9 \,cm$. Refractive index of water is $\mu_w = \frac{	ext{Real depth}}{	ext{Apparent depth}

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(C) For water, real depth $= 12 \,cm$. Apparent depth $= 9 \,cm$. Refractive index of water is $\mu_w = \frac{	ext{Real depth}}{	ext{Apparent depth}} = \frac{12}{9} = \frac{4}{3}$. When water is replaced by a liquid of refractive index $\mu_l = 1.5$, the new apparent depth is given by: $	ext{New apparent depth} = \frac{	ext{Real depth}}{\mu_l} = \frac{12}{1.5} = 8 \,cm$. The microscope was initially focused at $9 \,cm$ and now needs to be focused at $8 \,cm$. Therefore, the distance through which the microscope has to be moved is $9 \,cm - 8 \,cm = 1 \,cm$.

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