Refraction at Plane Surfaces — Part 2: Apparent depth, prisms and total internal reflection: visual lesson, ICSE Class 10 Physics (Science Paper 1)

Lesson

Things are not where they seem

Part 2 — refraction makes water look shallow, lets a prism bend light towards its base, and, past a certain angle, stops light leaving glass at all.

In this lesson you will

Use refractive index = real depth / apparent depth and explain why a pool looks shallower
Trace a ray through a triangular prism and mark the angle of deviation
State the conditions for total internal reflection and calculate the critical angle
Explain how right-angled isosceles prisms turn light through 90 and 180 degrees

Table of four observations and the idea from this part that explains each
Observation	Idea
A pond looks shallower than it is	Real and apparent depth
A prism bends a beam towards its base	Deviation
A diamond sparkles	Total internal reflection
A periscope uses prisms, not mirrors	Totally reflecting prisms

Diagram

Real and apparent depth

Rays from a coin at the bottom of a pool bend away from the normal as they leave the water. Produced backwards, they meet at a point above the coin, so the coin appears raised: the pool looks shallower. For viewing from directly above, $\mu = \frac{\text{real depth}}{\text{apparent depth}}$ The shift (apparent rise) $= \text{real depth} - \text{apparent depth} = \text{real depth}\left(1 - \dfrac{1}{\mu}\right)$ . Viewed obliquely, the object appears raised even more.

Worked example

Worked example: a fish tank

Problem. A small pebble lies at the bottom of a fish tank filled with water ( $\mu = \frac{4}{3}$ ) to a depth of 36 cm. (a) How deep does the pebble appear when viewed from directly above? (b) By how much does it appear raised?

(a) $\text{apparent depth} = \dfrac{\text{real depth}}{\mu} = \dfrac{36}{4/3} = \dfrac{36 \times 3}{4} = 27\ \text{cm}$ .

(b) $\text{shift} = 36 - 27 = 9\ \text{cm}$ .

Table of the values in the fish tank example
Quantity	Value
Real depth	36 cm
Refractive index of water	4/3
Apparent depth	27 cm
Apparent rise of the pebble	9 cm

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