Sec 4 Physics Reflection & Refraction notes

A ray hitting a plane mirror bounces with the angle of incidence equal to the angle of reflection, both measured from the normal (the line at 90° to the surface). The incident ray, the reflected ray and the normal all lie in the same plane. These two statements are the laws of reflection. Beware the classic trap: if a question gives the angle between ray and mirror, subtract from 90° first — a ray meeting the mirror at 30° to the surface has an angle of incidence of 60°.

The image in a plane mirror has four fixed properties: it is virtual (rays only appear to come from it), upright, the same size as the object, and laterally inverted (left and right swap). The image is exactly as far behind the mirror as the object is in front. In smooth surfaces the reflection is regular; on rough surfaces like paper the same law applies microscopically but the normal points every which way, scattering light in all directions — diffuse reflection — which is why rough surfaces are visible from any angle but do not form images.

Light travels at c = 3.0 × 10⁸ m/s in vacuum but slower in every material medium. The crossing of a boundary at an angle turns that speed change into a direction change: entering a denser medium the ray bends toward the normal; leaving into a less dense medium it bends away. The frequency never changes (the source sets it); the speed and wavelength fall together inside the denser medium, linked by v = fλ.

Two equations quantify refraction. For a ray going from air (or vacuum) into a medium at incidence i and refraction r: n = sin i ÷ sin r, the refractive index. And comparing speeds: n = c ÷ v, where v is the speed of light in the medium. A bigger n means optically denser: more slowing, stronger bending, lower speed. Typical values: water 1.33, glass about 1.5, diamond 2.4.

Refraction shows up everywhere you look — literally. A pencil standing in a glass of water appears bent at the surface because light leaving the water bends away from the normal on its way to your eye. A pool looks shallower than it is: rays from the bottom bend away from the normal leaving the water, so the bottom appears raised. The apparent depth relates to the real depth through n = real depth ÷ apparent depth — which is exactly why a 1.2 m deep pool of water looks only about 0.9 m deep.

A ray travelling inside a denser medium toward a less dense one (glass to air, water to air) partly reflects and partly refracts away from the normal. As the angle of incidence grows, the refracted ray weakens and bends further until, at one special angle, it grazes along the boundary (angle of refraction = 90°). That incidence is the critical angle, c. Beyond it, refraction dies completely: all the light reflects back inside — total internal reflection.

The two conditions for TIR are therefore: (1) light travels from a denser to a less dense medium, and (2) the angle of incidence is greater than the critical angle. At exactly the critical angle the refracted ray travels along the surface; below it, normal refraction with a partial reflection.

The critical angle connects straight to refractive index: setting r = 90° in n = sin i ÷ sin r gives sin c = 1 ÷ n (for a medium-to-air boundary). Denser media have smaller critical angles: water (n = 1.33) c ≈ 49°, glass (n = 1.5) c ≈ 42°, diamond (n = 2.4) c ≈ 25°. Diamond’s tiny critical angle is why light entering a cut stone bounces around inside many times before escaping in bright flashes — the sparkle.

An optical fibre is a thin glass strand with a core of higher refractive index clad in a lower-index layer. Light injected at a shallow angle meets each wall at an incidence above the critical angle and bounces along by thousands of total internal reflections, even around gentle curves, arriving at the far end bright and intact. Telecommunications carry telephone and internet data as light pulses through fibres across oceans; medicine threads an endoscope — a bundle of fibres — into the body to image organs without surgery.

A 45°–45°–90° glass prism can replace a mirror: light hits the hypotenuse face at 45°, which is greater than glass’s ≈42° critical angle, so it is totally internally reflected and deviated by exactly 90°. Two prisms in a periscope shift the view up and over; prism binoculars fold a long light path into a short body and also invert the image the right way up. Prisms beat silvered mirrors because TIR reflects essentially all of the light (mirrors absorb a little) and never tarnish or peel.

The classic practical: shine a ray into a rectangular glass block, mark the entry and exit points, remove the block and draw the rays. Measure i and r with a protractor for several angles of incidence (say 20° to 60°). Refractive index for each pair comes from n = sin i ÷ sin r — and every pair should give the same n, because it is a property of the glass, not of the angle chosen.

A stronger analysis plots sin i (y-axis) against sin r (x-axis): the points form a straight line through the origin whose gradient is n. Averaging by gradient beats averaging single ratios — it uses every point at once and shows any rogue measurement instantly. Remember the geometry too: inside a rectangular block the ray is parallel to the original incident ray (equal refractions at both parallel faces cancel), but it is laterally displaced sideways.