Reflection and refractionIB MYP Physics: Revision notes

When light hits a surface it can be reflected. We draw a normal, a line at 90° to the surface at the point where the ray hits it, and measure all angles from the normal.

Law of reflection: the angle of incidence (i) equals the angle of reflection (r).

The incident ray, the reflected ray and the normal all lie in the same plane. Be careful: if a ray makes 30° with the mirror, the angle of incidence is 90° − 30° = 60°.

A plane mirror is a flat mirror. The image it forms is:

• virtual: it appears to be behind the mirror, and cannot be projected on to a screen (light does not actually pass through the image)
• the same size as the object
• the same distance behind the mirror as the object is in front
• laterally inverted: left and right are swapped, as when you raise your right hand and your image raises its left.

Refraction is the change in direction of a wave when it crosses a boundary between two materials, caused by a change in speed.

• Light entering a denser material such as glass or water slows down and bends towards the normal.
• Light leaving it speeds up and bends away from the normal.
• A ray along the normal (angle of incidence 0°) does not bend, but still changes speed.

Water waves refract too. When waves move from deep water into shallow water they slow down, the wavelength gets smaller and they bend towards the normal. The frequency does not change.

The refractive index (n) of a material tells us how much it bends light. For light going from air into the material:

n = sin i ÷ sin r

where i is the angle of incidence and r is the angle of refraction. It has no units. A larger n means more bending.

Example: i = 45° and r = 28°. n = sin 45° ÷ sin 28° = 0.707 ÷ 0.469 = 1.5.

To find r: i = 30° in glass with n = 1.5 gives sin r = sin 30° ÷ 1.5 = 0.333, so r = 19.5°.

When light travels from glass towards air, it bends away from the normal. As the angle of incidence increases, the angle of refraction increases until it reaches 90°. The angle of incidence at which this happens is the critical angle (about 42° for glass).

If the angle of incidence is greater than the critical angle, no light leaves and all of it is reflected back into the glass. This is total internal reflection. It only happens when light travels towards a less dense material.

Optical fibres are thin strands of glass. Light signals enter at one end and hit the wall at angles greater than the critical angle, so they are totally internally reflected along the fibre and zigzag to the other end. They are used for fast internet and telephone signals, and for endoscopes in medicine.

Prisms: a glass prism with 45° angles has a critical angle of 42° so light that hits the long face at 45° is totally internally reflected. Prisms are used in periscopes and binoculars.