Reflection

Angles of reflection and incidence

Reflection is when light 'bounces' off a material which is different to the one in which it is travelling. You may remember from GCSE (or equivalent) level that we can calculate the direction the light will take if we consider a line known as the 'normal'. The normal is perpendicular to the boundary between the two materials, at the point at which the light is reflected. The angle between the normal and the ray of light is known as the angle of reflection (r). The ray of light will be reflected back at the same angle as it arrived at the normal, on the other side of the normal.

Refraction

Refraction is when light changes velocity when it travels across the boundary between two materials. This causes it to change direction. The angle between the normal and the refracted ray of light is known as the angle of refraction (r).

The Refractive Index

The refractive index is a measure of how much light will be refracted on the boundary between a material and a 'reference material'. This reference material is usually either air or a vacuum. It is given by the following formula:

$n = \frac{c_0}{c_1}$

where c0 is the speed of light in a vacuum (3 x 108 m/s) and c1 is the speed of light in the material.

Snell's Law

We can relate the refractive index to the angles of incidence (i) and refraction (r) using the following formula, known as Snell's Law:

$n = \frac{\sin{i}}{\sin{r}} = \frac{c_0}{c_1}$

Total Internal Reflection

Normally, when light passes through a non-opaque material, it is both reflected and refracted. However, sometimes, rays of light are totally internally reflected; in other words, they are not refracted, so no light goes outside the material. This is useful in optic fibres, which allow a signal to be transmitted long distances at the speed of light because the light is totally internally reflected.

Critical Angle

The critical angle is the minimum angle of incidence, for a given material, at which rays of light are totally internally reflected. At the critical angle (C), the angle of refraction is 90°, as any smaller angle of incidence will result in refraction. Therefore:

$n = \frac{\sin{90}}{\sin{r}}$

Since sin 90° = 1:

$n = \frac{1}{\sin{r}}$

$\sin{r} = \frac{1}{n} = \sin{C}$

In word form, in a material with refractive index n, light will be totally internally reflected at angles greater than the inverse sine of the reciprocal of the refractive index.

Questions

1. A ray of light is reflected from a mirror. Its angle to the normal when it reaches the mirror is 70°. What is its angle of reflection?

2. The speed of light in diamond is 1.24 x 108 m/s. What is its refractive index?

3. The refractive index of ice is 1.31. What is the speed of light in ice?

4. A ray of light passes the boundary between air and a transparent material. The angle of refraction is 20°, and the angle of incidence is 10°. What is the speed of light in this material? Why is it impossible for this material to exist?

5. What is the critical angle of a beam of light leaving a transparent material with a refractive index of 2?

Worked Solutions