A pond appears to be 2.7 m deep. If the refractive index of water is 4 3 , find the actual depth of the pond.
Topic: Refraction / total internal reflection
Answer
Given: apparent depth = 2.7 m, refractive index of water μ = 4/3
μ = real depth ÷ apparent depth
4/3 = real depth ÷ 2.7 real depth = (4/3) × 2.7 = 4 × 0.9 = 3.6 m
Actual depth of the pond = 3.6 m
Refraction makes a pond look SHALLOWER than it is, so the real depth must be the bigger number. Multiply the apparent depth by μ; dividing gives 2.025 m, which would mean the water looks deeper than it is — the opposite of what actually happens.
Use that physical check every time rather than trying to remember which way the formula goes. Real depth is always greater than apparent depth when you look into water from air.
The same relation gives the apparent "rise" of an object: rise = real − apparent = 3.6 − 2.7 = 0.9 m.