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(C) The focal length of a mirror depends only on its radius of curvature $(f = R/2)$ and is independent of the refractive index of the surrounding med

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Focal length of the mirror remains unchanged, while the focal length of the lens increases.

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(C) The focal length of a mirror depends only on its radius of curvature $(f = R/2)$ and is independent of the refractive index of the surrounding medium. Therefore, the focal length of the concave mirror remains unchanged in water.However, the focal length of a lens is determined by the Lens Maker's Formula: $1/f = (n_g/n_m - 1)(1/R_1 - 1/R_2)$, where $n_g$ is the refractive index of the lens material and $n_m$ is the refractive index of the medium. Since the refractive index of water $(n_m \approx 1.33)$ is greater than that of air $(n_m \approx 1.0)$, the relative refractive index $(n_g/n_m - 1)$ decreases, causing the focal length of the convex lens to increase.

$A$ concave mirror and a convex lens are held in water. What changes, if any, do you expect in their focal length?

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