Physics · Lesson 18

Refraction and lenses

JAMBWAECNECO

What the syllabus asks

JAMB: reflection, plane and curved mirrors, refraction, refractive index, critical angle, prisms, lenses, optical instruments, defects of vision, dispersion

WAEC: rectilinear propagation of light (shadows, eclipses, pinhole camera), reflection at plane and curved mirrors, mirror formula and magnification, refraction, laws of refraction, refractive index, real and apparent depth, total internal reflection and critical angle, refraction through prisms, lenses (converging and diverging), lens formula, power, optical instruments, the eye and its defects,…

NECO: rectilinear propagation of light (shadows, eclipses, pinhole camera), reflection at plane and curved mirrors, mirror formula and magnification, refraction, laws of refraction, refractive index, real and apparent depth, total internal reflection and critical angle, refraction through prisms, lenses (converging and diverging), lens formula, power, optical instruments, the eye and its defects,…

What you will learn

Explain shadows, eclipses and the pinhole camera using rectilinear propagation.
State the laws of reflection and describe images in plane and curved mirrors.
Use the mirror and lens formula with the real-is-positive sign convention.
State Snell's law and solve problems on refractive index and apparent depth.
Explain total internal reflection, calculate the critical angle and describe its uses.
Describe image formation by converging and diverging lenses, and calculate power.
Explain the eye, its defects and their correction, simple optical instruments and dispersion.

Key points

Light travels in straight lines: shadows (umbra, penumbra), eclipses, pinhole camera m = v/u.
Reflection: i = r, measured from the normal; plane mirror image virtual, upright, same size, laterally inverted.
Rotating a mirror by θ turns the reflected ray by 2θ; inclined mirrors give 360/θ − 1 images.
Concave mirrors converge (shaving, headlamps); convex mirrors diverge (driving mirrors); r = 2f.
1/f = 1/u + 1/v, m = v/u; real-is-positive, virtual distances and diverging focal lengths negative.
Refraction: n = sin i / sin r = c/v = real depth / apparent depth; n₁ sin θ₁ = n₂ sin θ₂.
TIR: denser to less dense, i > C, sin C = 1/n; used in fibres, prisms, explains mirages and sparkle.
Prism: n = sin((A + Dm)/2)/sin(A/2); violet deviates most; dispersion gives ROYGBIV.
Converging lens: real images beyond F, magnifying glass inside F; diverging lens: virtual, diminished.
P = 1/f (m), dioptres; myopia → diverging lens; hypermetropia → converging lens.
Magnifier M = 1 + D/f; telescope M = fo/fe, length fo + fe.

Start here: Light travels in straight lines

On a dusty harmattan morning, sunlight streaming through a gap in a window makes a sharp, straight beam. Light travels in straight lines in a uniform medium: rectilinear propagation. A thin line of light is a ray; a collection of rays is a beam, which may be parallel (from the Sun), converging or diverging (from a bulb).

Materials are transparent (glass, clean water: let light through clearly), translucent (frosted glass, oiled paper: let light through but scatter it) or opaque (wood, metal: block it). Opaque objects cast shadows.

A point source gives a sharp shadow called the umbra (total shadow).
An extended source gives a dark umbra surrounded by a partly lit penumbra.

Eclipses

In a solar eclipse, the Moon passes between the Sun and the Earth and its shadow falls on part of the Earth. People in the umbra see a total eclipse; those in the penumbra see a partial eclipse. In a lunar eclipse, the Earth comes between the Sun and the Moon, and the Moon moves into the Earth's shadow. Nigeria witnessed a total solar eclipse in March 2006, when day became dark for a few minutes.

The pinhole camera

A box with a tiny hole at the front and a translucent screen at the back forms a real, inverted image, because rays from the top of the object pass straight through the hole to the bottom of the screen. Its magnification is

m = image height / object height = image distance / object distance

Making the hole larger makes the image brighter but blurred, because several overlapping images form. Moving the screen further from the hole makes the image larger but dimmer.

Worked example 18.1

A pinhole camera is 15 cm long. It photographs a 9 m tall palm tree 45 m away. Find the image height.

m = image distance / object distance = 0.15/45 = 1/300. We use similar triangles because the rays are straight lines through the hole.
Image height = 9 × 1/300 = 0.03 m = 3 cm.

3 cm (inverted)

⚠️ Common mistake: mixing units: convert all distances to the same unit before dividing.

Try it yourself. What happens to the image in a pinhole camera if a second hole is made beside the first?

Show solution

Two overlapping images form, side by side.

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Practice questions

1. An object 40 cm from a concave mirror of f = 10 cm. Find v and m.

Show worked answer

1/v = 1/10 − 1/40 = 3/40, v = 13.3 cm; m = 0.33.

2. Find the critical angle of water (n = 4/3).

Show worked answer

sin C = 0.75, C ≈ 48.6°.

3. A ray in air strikes glass (n = 1.5) at 30°. Find r.

Show worked answer

sin r = 0.5/1.5 = 0.333, r ≈ 19.5°.

4. A fish is 1.2 m below the water surface (n = 4/3). How deep does it appear?

Show worked answer

1.2 × 3/4 = 0.9 m.

5. An object 12 cm from a converging lens of f = 8 cm. Find v and m.

Show worked answer

1/v = 1/8 − 1/12 = 1/24, v = 24 cm; m = 2.

Key words

Ray: The path along which light energy travels, drawn as a line with an arrow.
Normal: A line at 90° to a surface at the point where a ray strikes.
Real image: An image formed where rays actually meet; can be caught on a screen.
Virtual image: An image formed where rays only appear to come from; cannot be caught on a screen.
Lateral inversion: The left–right reversal of an image in a plane mirror.
Principal focus (F): Point where rays parallel to the axis meet (or appear to diverge from) after reflection or refraction.
Focal length (f): Distance from the pole of a mirror or optical centre of a lens to F.
Radius of curvature (r): Radius of the sphere of which a curved mirror is part; r = 2f.
Magnification (m): Image height ÷ object height = v/u.
Refractive index (n): Ratio sin i / sin r, or speed of light in vacuum ÷ speed in the medium.
Critical angle (C): Angle of incidence in the denser medium for which the angle of refraction is 90°.
Total internal reflection: Complete reflection of light inside a denser medium when i > C.

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