A liquid of refractive index n fills a tank with a plane mirror on its bottom. A point object P sits on the liquid surface, at a height h above the mirror. An observer looks vertically down from above and sees the object and its image. How much distance does the observer note between P and its imag…

Question

A liquid of refractive index n fills a tank with a plane mirror on its bottom. A point object P sits on the liquid surface, at a height h above the mirror. An observer looks vertically down from above and sees the object and its image. How much distance does the observer note between P and its image?

Accepted Answer

(2) (2h)/n. Given: liquid of refractive index n and depth h, a plane mirror on the bottom, the point object P on the surface, and the observer looking straight down from the air. Idea: first find where the mirror puts the image, then ask how deep that image looks through the liquid. A plane mirror images a point as far behind itself as the point is in front, so the image lies h below the mirror -- a real depth of 2h below the surface. Light reaching the observer from that image has gone h down and h back up inside the liquid, a full 2h of liquid path. Apparent depth is real depth divided by n, so the image appears at (2h)/n below the surface. P is on the surface itself and is not displaced at all, so the separation the observer notes is (2h)/n.

Step-by-step solution

Why the other options are wrong