Light can be thought of as travelling in rays that change direction through reflection and refraction. Reflection occurs when light strikes a surface, following the laws that the angle of incidence equals the angle of reflection. Refraction occurs when light passes from one medium to another of different density, bending according to Snell's law that relates the sine of the angle of incidence to the sine of the angle of refraction through the refractive indices. The refractive index quantifies how much light slows down in a medium relative to a vacuum. Common refractive indices include air as 1, water as 1.33 and glass around 1.5.
2. Introduction
To explain how light behaves, we can think of light
travelling as rays.
A ray travels in a straight line. It will change direction
if:
• It is reflected (when it strikes a surface)
• It is refracted (when it passes from one material to
another).
We can also think of light as waves
Laws of reflection
The laws of reflection tells us where a ray will go when
it is reflected.
The normal is the line at 90o to the reflecting surface
at the point where the incident ray strikes it
2
3. 3
normal
incident ray reflected rayi r
Law 1: angle of incidence = angle of reflection, i = r
(angles measured from the normal to the ray)
Law 2: incident ray, reflected ray and the normal are all
in the same plane.
These laws not only apply for flat surfaces but also for
curved and rough surfaces
normal
i r i
r
4. Refraction: when it happens
Light travels fastest in a vacuum. It travels more slowly
in other media.
When light changes speed (because it travels from one
medium to another), it is refracted.
• If a ray enters a medium head-on (angle of incidence i
= 0), it travels straight on.
• If a ray enters a medium obliquely, it bends
Laws of refraction
As with reflection, angles are measured from the normal
to the ray.
Law 1: Snell’s law explains how the angles of incidence
and refraction are related.
Law 2: incident ray, refracted ray and the normal are all
in the same plane.
4
5. 5
normal
r r
i i
Note that r is now the angle of refraction, not reflection
Refractive index n
The refractive index, n of a medium relates the speed
of light in the medium to the speed of light in free space
(vacuum)
Refractive index, n =
speed of light in free space
speed of light in medium
n =
c0
cmedium
6. Refractive index n
In a medium of refractive index 2, light travels at half
its speed in free space (vacuum). Some values of n are
worth remembering:
n0 = 1 (by definition)
nair = 1.00 (to 2 decimal places)
nwater = 1.33
nglass ~ 1.5 (depending on the composition of glass)
Snell’s law
For a ray passing from air into a medium of refractive
index n, the angle of incidence i and the angle of
refraction r are related by:
6
n =
sin i
sin r
7. Snell’s law
When a ray passes from one medium to another, the
refractive index can be calculated using the equations:
7
n =
ci
cr
=
nr
ni
Example
A ray of light travels from glass (ni = 1.5) into water
(nr = 1.33) with an angle of incidence i of 30o. Calculate
the angle of refraction r.
Step 1: calculate the relative refractive index from the
values for the two materials:
n =
nr
ni
=
1.33
1.5
= 0.887
8. 8
Step 2: Substitute values into the Snell’s law
equation, rearrange and solve:
n = sin i
sin r
so 0.887 =
sin 30o
sin r
sin r = sin 30o
0.887
= 0.504 so r = 34o
Questions:
1. Does a ray speed up or slow down when it enters a
more dense medium?
2. If the angle between the incident ray and the
reflective surface of a mirror is 35o, what are the
angles of incidence and refraction?
3. A ray of light, travelling through air, strikes a glass
surface with an angle of incidence of 40o. The
refractive index of glass is 1.47. draw a diagram to
show the situation. Calculate the angle of refraction.
