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Light

13 min read

Refraction of light

Refraction is the bending of light when it passes from one transparent material into another, because its speed changes. Light entering a denser material (air to glass) slows down and bends towards the normal. Leaving a denser material it bends away from the normal.

Refraction of lightA ray of light travelling in air hits the surface of glass. It bends towards the normal as it enters the denser glass, so the angle of refraction r is smaller than the angle of incidence i. The relationship is sine of i divided by sine of r equals a constant, the refractive index.irairglassnormalincident rayrefracted rayn = sin i ÷ sin r
Snell's law: n is the refractive index of the second material (relative to the first), i the angle of incidence, r the angle of refraction, c the speed in air and v the speed in the material. Water n ≈ 1.33, glass n ≈ 1.5, diamond n ≈ 2.4.
Try itSnell's law

Choose the angle of incidence in air and the refractive index. Find the angle of refraction and the critical angle for light going the other way.

Total internal reflection

When light goes from a denser to a less dense material, the angle of refraction is larger than the angle of incidence. At the critical angle c the refracted ray runs along the surface (90°). At larger angles all the light is reflected: total internal reflection. Then sin c = 1 ÷ n.

Total internal reflectionThree rays inside glass hitting the boundary with air. A ray at a small angle mostly refracts out into the air. At the critical angle the refracted ray travels along the boundary. At a larger angle all the light is reflected back into the glass, which is total internal reflection.airglassi < c: mostly refracts outi = c (critical angle)i > c: total internal reflection
ApplicationHow it works
Optical fibresLight is trapped in a thin glass thread by repeated total internal reflection: telephone, internet and endoscopes
Prisms in binoculars and periscopesA 45° glass prism reflects light through 90° or 180° without loss
Reflectors on bicycles and roadsPlastic corner reflectors return the light to its source
Diamonds sparkleThe critical angle is small (24°), so light is reflected many times inside

Lenses and image formation

A converging (convex) lens is thicker at the centre and brings parallel rays to a principal focus F. A diverging (concave) lens is thinner at the centre and spreads parallel rays out. The focal length f is the distance from the lens to F. Use three rays to find an image: one parallel to the axis (through F after the lens), one through the centre (undeviated) and one through F (emerging parallel).

A convex lens forms a real imageAn object arrow stands to the left of a convex lens at twice the focal length. A ray parallel to the axis passes through the focal point on the far side. A ray through the centre of the lens goes straight on. They meet beyond the lens and form a real, inverted image of the same size, also at twice the focal length.FF2F2Fobjectimage: real, inverted, same size
A concave lens forms a virtual imageAn object arrow stands to the left of a concave lens. A ray parallel to the axis bends away from the axis as if it came from the focal point on the object side. A ray through the centre goes straight on. The rays spread out, so the image is formed where their backward extensions meet: it is virtual, upright and smaller.Fobjectvirtual image: upright, smallerrays spread out
Object position (convex lens)Image
Beyond 2FReal, inverted, smaller, between F and 2F (camera)
At 2FReal, inverted, same size, at 2F
Between F and 2FReal, inverted, larger, beyond 2F (projector)
At FAt infinity (spotlight)
Inside FVirtual, upright, larger, same side as the object (magnifying glass)
Real-is-positive convention: u and v are distances from the lens; for a virtual image v is negative. Lens power P is in dioptres when f is in metres.
Worked exampleImage from a lens

An object is 30 cm from a convex lens of focal length 10 cm. Find the image distance and magnification.

  1. Use the lens formula.
  2. Magnification.

Answer: The image is 15 cm from the lens, real, inverted and half the size.

Try itLens calculator

Choose the focal length of a convex lens and the object distance. Find the image distance and the magnification.

Dispersion

White light is a mixture of colours. A glass prism bends violet light most and red light least, so white light is split into a spectrum of red, orange, yellow, green, blue, indigo and violet. This is dispersion. A rainbow is formed in the same way by raindrops.

Check yourself When light goes from air into glass it…
Check yourself The critical angle of a material with n = 2 is…
Check yourself An object is placed 5 cm from a convex lens of focal length 10 cm. The image is…

Key terms

Refractive index
The ratio sin i ÷ sin r, or c ÷ v.
Critical angle
The angle of incidence in the denser material for which the angle of refraction is 90°.
Focal length
The distance from a lens to its principal focus.
Dispersion
The splitting of white light into colours.

Summary

  • Refraction obeys Snell's law n = sin i ÷ sin r; light bends towards the normal in a denser material.
  • Total internal reflection occurs beyond the critical angle: sin c = 1 ÷ n; used in fibres and prisms.
  • Lens formula 1/f = 1/u + 1/v; magnification m = v/u.
  • A prism disperses white light into a spectrum.
Friction Optical Instruments