A rectangular glass block of refractive index 1.5 has an air bubble trapped inside it as shown in the diagram. When seen from the surface AB, it appears to be 4 cm deep.
Calculate the actual depth of the air bubble from the surface AB.
Topic: Real and apparent depth
Answer
Given: refractive index of glass μ = 1.5, apparent depth = 4 cm
μ = real depth ÷ apparent depth
1.5 = real depth ÷ 4 real depth = 1.5 × 4 = 6 cm
Actual depth of the air bubble from AB = 6 cm
Refraction makes the bubble look CLOSER to the surface than it is, so the real depth must be the larger number — multiply by μ rather than dividing. Dividing gives 2.67 cm, which would mean it looks deeper than it is.
The same relation works for a coin in water or a pond's floor; the medium does not matter, only the refractive index.
The apparent shift here is 6 − 4 = 2 cm.