) is equal
to the angle of reflection (
) and
the incident ray and the reflected ray both lie in the same plane (R) normal
to the surface (P).Interdisciplinary Project The Light
M A T H E M A T I C S
Reflection of light
The ray of light which strikes a surface (P) reflects in a way that
the angle of incidence () is equal
to the angle of reflection () and
the incident ray and the reflected ray both lie in the same plane (R) normal
to the surface (P).
 |
-angle of incidence - angle
between s and n - angle of reflection
- angle between n and the reflected ray |
Reflected light is always less intense from incident light because an amount of energy from incident light transfers into another media.The law of reflection can be derived from Fermat`s principle, which says that the light travels between two points so that the time taken is a minimum.
The time needed for light to travel from A to B:
From the condition for a minimum:
which means that: sin =
sin , or =
.
Let us compare the length of path ACB (in which the angle of incidence is equal to the angle of refraction), with the length of any other path:
 |
(right-angled triangles with equal corresponding legs) Therefore: AD = A1D..(2) |
Instead of paths ACB and ADB, we can consider paths A1DB=A1B. According to the rule which says that the shortest path connecting two points is a straight line, light "chooses" the shortest possible path.
 |
All rays of light moving parallely to the axis of a parabola pass through one common point - the focus of the parabola. This property of parabolic reflection of light is widely used in solar devices for heating, telescopes, radars... |
 |
If the light source is situated in the focus of the parabola,
the rays of light are reflected
parallely. This is used in parking lights, torches etc. |
| Entertain your friends by looking through opaque objects: books, palm of hand, etc. |  |
The above phenomenon is explained by multiple reflection of a ray of light using mirrors. Many "magic" tricks are based on this principle, but also optical instruments, e. g. periscope.
Refraction of light
Refraction of light occurs on the border of two media because light travels at different speeds in different materials.
n1- index of refraction of the first medium n2 - index of refraction of the second medium n1 < n2 |
- angle of incidence
s - incident ray l - refracted ray |
The laws of refraction:
for all rays of fixed wavelength. The constant ratio is called the relative refractive index. |
When a ray of light travels from an optically less dense medium to a more dense medium, it bends towards the normal and the ray of light refracts for an arbitrary angle of incidence. If the ray travels from a denser medium to a less dense medium, it bends away from the normal. There is a so-called critical angle of incidence for which the angle of refraction is 90°.
Phenomenon of total internal reflection
An incident ray striking a boundary from a more refractive medium to
a less refractive medium at an angle greater than
,
experiences total reflection.
According to Snell's law, in this case the angle of refraction must be greater than the angle of incidence. If the angle of incidence is such that the angle of refraction is greater than 90°, total internal reflection takes place.
Optical prism
If light passes through a prism, a transparent object with flat, polished surfaces at angles to each other, the exit ray is no longer parallel to the incident ray.
The angle between the path of the incident ray and the path of the emergent
ray is the angle of deviation 
.
The angle of deviation d depends on the angle of the prismand
the refractive index of the material of the prism. By measuring and
, the refractive
index of the material of the prism can be calculated. It can be shown that
the deviation is a minimum when the light passes symmetrically through
the prism.
The prism for total internal reflection is a 45°-45°-90° prism which can turn a light ray for 90° or 180° degrees.
