At a glass-to-air boundary, some light always reflects back inside
Definition
Internal reflection
The reflection of light back into a material at a boundary with a material in which light travels faster, such as glass to air.
- When light inside glass reaches the boundary with air, it usually splits into two parts.
- A refracted ray escapes into the air, bending away from the normal because the light speeds up.
- A weaker internally reflected ray stays inside the glass, obeying i=ri = ri=r just like reflection at a mirror.
- At small angles the refracted ray is bright and the internally reflected ray is faint, which is why a window is mostly see-through.
- As the angle inside the glass grows, the refracted ray bends further from the normal and gets dimmer, while the internally reflected ray gets brighter.
- Internal reflection only happens on the way out of the slower material, so light going from air into glass can never do it.
The critical angle is the tipping point where light can no longer escape
Definition
Critical angle
The angle of incidence inside the denser material for which the angle of refraction in the less dense material is exactly 90∘90^\circ90∘. Symbol ccc.
- Keep increasing the angle inside the glass and the refracted ray swings further and further round, closer and closer to the glass surface.
- At the critical angle it lies flat along the surface, grazing the boundary at 90∘90^\circ90∘ to the normal, and it is barely visible.
- There is no angle bigger than 90∘90^\circ90∘ available on that side of the boundary, so past the critical angle the refracted ray simply cannot exist.
- The critical angle is a property of the pair of materials: for ordinary glass to air it is about 42∘42^\circ42∘, for water to air about 49∘49^\circ49∘, and for diamond to air only about 24∘24^\circ24∘.
- A material that slows light more has a smaller critical angle, which is why diamond traps light so easily and sparkles.
Past the critical angle, every bit of the light is reflected
Definition
Total internal reflection
What happens when light strikes a boundary with a less dense material at an angle of incidence greater than the critical angle: no light is refracted out and all of it is reflected back inside.
- Two conditions must both be satisfied, and an answer that gives only one of them is incomplete.
- The light must be travelling from a denser material towards a less dense one, such as glass to air.
- The angle of incidence must be greater than the critical angle.
- The word total is doing real work: 100%100\%100% of the light is reflected, which makes it a better reflector than any silvered mirror, since a mirror always absorbs a little.
- The reflected ray still obeys the law of reflection, so the angle of reflection equals the angle of incidence inside the glass.
Watching it happen in a semicircular block
- Stand a semicircular glass block on paper, draw round it, and mark the centre point of its flat face with a normal drawn at 90∘90^\circ90∘ to that face.
- Aim a narrow ray at that centre point through the curved side, so it travels along a radius and enters without bending.
- That trick means the only refraction happens at the flat face, so the angle you set is exactly the angle the light meets that boundary at.
- Swing the ray box slowly round the curved edge, keeping the beam aimed at the centre, and watch three stages appear.
- A bright ray leaves the flat face, bent away from the normal, alongside a faint reflected ray inside the glass.
- At the critical angle the emerging ray grazes along the flat face and fades out, while the internal ray becomes bright.
- Past it, nothing leaves the flat face and the whole beam bounces back inside.
- Marking the ray at the moment it grazes the surface and measuring that angle from the normal gives you the critical angle of the glass.
Example
- Right-angled glass prisms in periscopes and binoculars turn light through 90∘90^\circ90∘, because the light meets the sloping face at 45∘45^\circ45∘, which is above glass's critical angle of about 42∘42^\circ42∘.
- Prisms are used instead of mirrors here because they reflect all the light and give a brighter, sharper image.
- A bicycle reflector uses two internal reflections to send a car's headlight beam straight back towards the driver.
- Light entering a diamond bounces round inside many times before escaping, because its critical angle of about 24∘24^\circ24∘ is so small.
- The same effect keeps a signal trapped inside an optical fibre along its whole length.
Common Mistake
- Do not give only one condition for total internal reflection; you need both the denser-to-less-dense direction and the angle greater than ccc.
- Do not define the critical angle as the angle where light stops refracting; it is the angle of incidence that gives an angle of refraction of exactly 90∘90^\circ90∘.
- Do not measure the critical angle from the glass surface; like every optics angle it is measured from the normal.
- Do not expect total internal reflection when light passes from air into glass, however large the angle.
- Do not confuse internal reflection with total internal reflection; the first happens at any angle alongside refraction, the second only above the critical angle and with no refraction at all.
Exam technique
- Compare the angle you are given with the critical angle first, because that single comparison decides whether you draw a refracted ray or not.
- In a prism question, mark the 45∘45^\circ45∘ angle at the sloping face and say it is greater than the critical angle, since that comparison is where the mark sits.
- When you draw total internal reflection, show no ray at all leaving the surface, because a faint escaping ray contradicts the word "total".
- Everyday example questions want a use plus the reason, so name the prism, fibre or reflector and then say the light meets the surface above the critical angle.
Self review
- State what is meant by the critical angle.
- Give the two conditions needed for total internal reflection.
- Describe what you see as the angle inside a semicircular block is slowly increased past the critical angle.
- Why is a glass prism used instead of a mirror in a pair of binoculars?
- Explain why light passing from air into glass can never be totally internally reflected.
