Explain why a coin at the bottom of a bucket of water appears raised. Derive the relation between real depth, apparent depth and refractive index.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · State the principle. Light from the coin passes from water (denser) into air (rarer), so it bends away from the normal.
2 · Draw the ray diagram. [Water surface; coin O at depth h on a vertical normal; ray OA bending away from the normal into air; dotted backward extension meeting the normal at I; mark i, r, h and h′]
3 · Write the geometry.
tan r = x/h
tan i = x/h′
4 · Apply Snell's law for small angles.
n sin r = sin i
For near-normal rays sin ≈ tan, so n x/h = x/h′
5 · Write the result. h/h′ = n, so the apparent depth is h′ = h/n and the coin seems raised by h(1 − 1/n).
6 · Real life. A pond looks shallower than it is, so judging its depth by eye can be dangerous.
7 · Close in one line. The coin appears raised because the eye traces the bent rays back along straight lines.
Scoring tip: Always write 'near-normal viewing'. The result h′ = h/n holds only for small angles.
