Light: reflection, refraction and TIR

3.14–3.16

Light is transverse — and it reflects

Light waves are transverse and can be reflected and refracted (3.14). The law of reflection (3.15) is

Angle of incidence equals angle of reflection, both from the normal.

A full ray diagram (3.16) needs: a ruler-straight surface, a dashed normal at the point of incidence, arrows on both rays, and $i$ and $r$ marked from the normal — not from the mirror.

3.16–3.18

Refraction and Snell’s law

Refraction is a change of speed when a wave crosses a boundary. If it hits at an angle, the direction also changes.

• Air → glass (less dense → more dense): light slows down and bends towards the normal. So $r < i$.
• Glass → air: light speeds up and bends away from the normal.
• Along the normal ($i=0$), the ray does not bend; it still changes speed.

Refractive index of the material (for air–glass) is

$i$ is in air, $r$ is in glass, both from the normal. Glass is typically about $1.5$. If you get $n=0.67$, you have inverted the fraction.

3.17, 3.19 · Required practicals

Blocks, prisms, and measuring $n$

What each shape is for (3.17)

• Rectangular block — the standard $i$ and $r$ at two parallel faces; ray emerges parallel to the original direction but laterally shifted.
• Semi-circular block — ray aimed at the curved face along a radius hits the flat face from inside glass, so you can find the critical angle.
• Triangular prism — deviation and, with white light, dispersion into a spectrum. Also TIR in reflecting prisms.

Investigate $n$ of glass (3.19)

Apparatus: ray box, single slit, rectangular glass block, white paper, sharp pencil, protractor, ruler.

Method I mark

1. Draw around the block. Mark the point of incidence. Draw the normal.
2. Send a narrow ray in. Mark two dots on the incident ray and two on the emergent ray.
3. Remove the block. Join the dots. Draw the path inside the glass.
4. Measure $i$ and $r$ from the normal. Calculate $n=\sin i/\sin r$.
5. Repeat for at least five angles. Average $n$.

Errors and how to reduce them

• Thick pencil lines — use a sharp pencil and a narrow slit.
• Protractor not on the normal — draw a long, faint normal first.
• Block slips — hold it or use Blu Tack.
• Very small $i$ — $\sin i$ and $\sin r$ are both small, so percentage error is large. Use a range such as $20^\circ$–$60^\circ$.

3.20–3.22

Critical angle and total internal reflection

When light is in glass, heading for air, $r$ is larger than $i$. Increase $i$ and $r$ grows until $r=90^\circ$ — the ray skims along the boundary. That angle of incidence is the critical angle $c$ (3.21).

For $n=1.50$, $\sin c = 0.667$, so $c = 41.8^\circ$ (use $\sin^{-1}$).

TIR happens only if both are true

1. The ray travels from a denser medium towards a rarer medium (glass → air).
2. The angle of incidence is greater than the critical angle ($i > c$).

Then there is no refracted ray — the light is totally reflected inside, and $i=r$ still holds.

Check you can

Worked examples →