Reflection and the plane mirror
Virtual image — An image formed where light rays only appear to come from. It cannot be projected onto a screen, because no light actually passes through it.
Light travels in straight lines, and when it meets a surface it bounces off. The law of reflection is short: the angle of incidence equals the angle of reflection, and both are measured from the normal — the line drawn at right angles to the surface at the point where the ray hits.
Measuring from the normal rather than from the surface itself is a convention, but it is the convention every mark scheme uses. Measuring from the surface gives you the complement of the right answer, which looks plausible and is wrong.
The image in a plane mirror has four properties worth learning as a set: it is the same size as the object, the same distance behind the mirror as the object is in front, laterally inverted (left and right swapped), and virtual.
Real or virtual: one test
A real image forms where light rays actually meet, so it can be caught on a screen — a cinema projection, or the image on a camera sensor. A virtual image forms where rays only appear to originate, so no screen will show it. "Can it be put on a screen?" is the question examiners are testing.
Refraction
Light changes speed when it crosses from one transparent material into another, and if it arrives at an angle, that change of speed bends it. This is refraction.
The rule for the direction is worth memorising as a pair. Going into a denser medium — air into glass or water — the light slows and bends towards the normal. Coming out into a less dense medium it speeds up and bends away from the normal.
A ray passing through a rectangular glass block therefore emerges parallel to the way it went in, having been shifted sideways. It bends one way going in and the opposite way coming out, and the two cancel.
Refraction is why a straw in a glass of water looks bent and why a swimming pool looks shallower than it is. Light from the submerged part bends as it leaves the water, but the eye assumes light has travelled in a straight line and traces it straight back — placing the object somewhere it is not.
- n
- refractive index
- i
- angle of incidence°
- r
- angle of refraction°
- c
- critical angle°
Increase the angle of incidence from inside the denser medium and watch the refracted ray bend further from the normal. Past the critical angle it disappears entirely and all the light reflects back inside.
Total internal reflection
Send light from glass towards air and increase the angle of incidence. The refracted ray bends further and further from the normal, until at one particular angle it grazes along the boundary itself. That angle is the critical angle.
Push past it and the refracted ray vanishes: all the light is reflected back into the glass. This is total internal reflection, and it happens only when two conditions are met together. The light must be travelling from the denser medium towards the less dense one, and the angle of incidence must exceed the critical angle. Both conditions must be stated to earn full marks.
The critical angle depends on the refractive index. The higher the index, the smaller the critical angle, and the more easily total internal reflection occurs. For glass it is about 42°, for water about 49°, and for diamond only 24° — which is why cut diamonds sparkle so brilliantly.
Light travels from glass of refractive index 1.50 towards air. Find the critical angle. State and explain what happens to a ray meeting the boundary at 50°.
- Use
sin c = 1/n.The critical angle is defined for the denser-to-less-dense boundary. sin c = 1/1.50 = 0.667.c = 41.8°.About 42° for ordinary glass.- 50° is greater than the critical angle, and the light is going from denser to less dense.Both conditions — state them explicitly.
- So total internal reflection occurs and no light emerges.
c = 41.8°, so at 50° the light is totally internally reflected
Optical fibres and lenses
An optical fibre is a thin glass core surrounded by cladding of lower refractive index. Light entering at a shallow angle strikes the core–cladding boundary above the critical angle, reflects totally, strikes the other side, reflects again — and so travels the whole length of the fibre even round bends, losing almost nothing.
This is how the internet crosses oceans and how an endoscope lets a surgeon see inside a patient without opening them up. Compared with copper wire, optical fibres carry far more data, lose far less signal over distance, and are immune to electrical interference.
A converging lens is thicker in the middle and brings parallel rays to a focus at the principal focus. The distance from the lens to that point is the focal length. Where the image forms, and whether it is real or virtual, depends entirely on where the object sits relative to the focal length.
Two cases cover most questions. An object further from the lens than the focal length produces a real, inverted image that could be caught on a screen — this is how a camera and the human eye work. An object closer than the focal length produces a virtual, upright, magnified image — this is a magnifying glass.
Key points
- Angles are always measured from the normal, never from the surface.
- Into a denser medium: slows down, bends towards the normal.
- Total internal reflection needs denser-to-less-dense AND an angle above the critical angle.
sin c = 1/n, so a higher refractive index means a smaller critical angle.- Object beyond the focal length gives a real inverted image; inside it, virtual and magnified.