This unit is about mirror dynamics and refraction.


The real is + sign convention

The formulae states that


Where F is focal length, U is the object distance from the pole and V the image distance from the pole.


For concave mirror, F is in front of the mirror and hence F is real and positive, the object is real image hence V is positive. If image is behind the mirror, it is virtual hence V is negative.

For convex mirrors, F is always behind the mirror and hence virtual the reform F is negative; the object is always placed in front of the mirror, it is real and hence U is positive; all image formed are behind the mirror hence virtual and there for V is negative.

Uses of concave mirror

  1. Small concave mirrors are used by dentists to examine teeth. The image is enlarged and upright when the teeth are positioned between the mirror and principles focus.
  1. Large can cave mirrors are used as shaving mirrors or make mirrors
  1. A concave reflector of an electric torch produces a parallel beam of light this principle is used in search lights, car head lights etc.
  1. The concave dishes are used to concentrate solar energy in solar cookers.
  1. Radio waves and other micro waves such as TVs signals. Internet etc from the atmosphere detected by concave receiving dishes called radio telescope. The dishes concentrate the waves to focus, where a detector placed at the focus transfer a signal to amplifying equipment.
  1. Concave wire mesh reflectors used collect television signals for domestic viewing
  1. Convex mirrors are used as rare view mirrors in cars, monitoring mirrors in super markets and so on. These mirrors give a wider view than the plane mirror
  1. They give up right images which are diminished. Making judgment of distance difficult.

Measuring focal length of a concave mirror

Using a distant object

This method is less accurate

mirror 1

The object at a distance [e.g. a free or a plant outside a lab] can be used to estimate the focal length of a concave mirror. Light rays from this object are parallel and from an inverted, diminished and real image of the object at the principle focus.

The image can be seen of a movable screen. The distance between the screen and mirror is measured and is approximately equal to the focal length of the mirror

Using a pin placed at c

mirror 2

The pin is fixed in cork such that its tip is at the same horizontal level as the centre of the mirror. Position is formed by moving the pin to or from the mirror for which these number parallax between the pin and its real image formed the distance between the pin, its image , the mirror is equal to r where; r = 2f hence f = ½r

mirror 3

A concave mirror is set up in a mirror holder. In front of the object the object used is a hole and cross wire in a white screen illuminated by a light bulb. Light from the object [cross wire] is passed onto the covered mirror and is reflected back onto the screen. This may give a faint [blurred] image of the crosswire on the screen. The position of the mirror is adjusted [sometimes the position of screen may be adjusted] until a sharp clear image of the object is formed on the screen alongside the object. The distance between the mirror and screen is equal to radius of curvature r or 2f


Refraction is the change in the direction of the path of light when it passes from one medium to another. This bending of the path of light is due to a change in the speed of light. When light passes from medium of light to another. When a ray passes from one medium to a more optically dense medium, the ray hence towards the normal conversely, a ray passing through from water or glass to a rather it is bent away from the normal.

The following are some effects that are attributed to refraction

mirror 4    

  1. The bend appurtenance of a straight struck when placed in water
  2. Swimming pool appears shall owe than it actually is
  3. Formation of a rainbow
  4. The appearance of land scope, shimmers or mirages on a hot summer’s day is due to refraction.

Common terms used in refraction are;-

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AO is called the incident ray

OB is the refracted ray

NN is the normal

Angle I is the angle of incidence while angle r is the angle of refraction

The laws of refraction;

Law 1:

States that the incident ray and the refracted ray are on opposite sides of the normal at the point of incidence and all the three are in the same plane.

Law 2 [Snell’s law]

The ratio of the sine of the angle of incidence to the site of the angles of refraction is a constant for a given pair of media

Snell’s law = sin i/ sin i  = constant

An experiment to investigated smell’s law


-Rectangular glass blocked

-4 optical pins

-White sheet of paper

-Soft board

-4 drawing pins

-Graph paper

-Mat hermetical instruments

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-Place the glass black on the white sheet of paper that is fixed onto a soft board by using the drawing pins

-Fix pins p1 and p2 in the white sheet of paper as far as possible along a line draw to represent the incidence ray

-Looking through the blocks from the other side fix the sighting pins E1 and E2 such that they appear to be in line with the image I1 and I2 of pins p1 and p2.

-Make the positions of all the pins then remove the glass block and join the pins E1 and E2 to the line TT1. Also join point O to where line E1 and E2 meet with.

-Measure the angles i and r and record

-Repeat the above procedure for angles of incidence and include the result in a table as below

i/0 r/o Sin i Sin r
25 15 0.42 0.25 6.8
30 20 0.5 0.34 1.47
35 24 0.57 0.41 1.39
40 29 0.64 0.48 1.33



The ratio  sin i/sin r should be practically constant

Plot a graph since i against sine r and find its gradient [slope]


Refractive index[n]

The refractive index is denoted by letter n. the refractive index is the value of the constant  for a ray passing one medium to another.

If a ray is passing a vacuum/air to another medium e.g. glass/ water then the refractive index calculated is called the absolute refractive index of the second medium with respect to vacuum or air.


If a ray posses from air to another medium then we talk of refractive index of the second medium. However, strictly speaking ‘absoluter refractive index’ is when the first medium is a vacuum.

If a ray posses from air to water then the refractive index of water is written as;-

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If a ray is incident at right angles to the boundary or the interface to the two mediums it cannot be refracted


mirror 8

mirror 9

Appearance of a straight rod/rule in water

mirror 10

Rays of straight light from B on a straight line pass through water to air. They are bent away from the normal at the boundary D. as the rays enter the eye they appear to be coming from point C which is above point B under the surface of water. Thus the rod appear bent at a due to this change in direction of light [refraction].

mirror 11

mirror 12

mirror 13

Real or apparent depth

Water in a pond appears shallower than it is. When a glass blocks is put on a page, the letter appear to be displaced upwards, these observation are  a result of reflection of light as it moves from one medium to another. This can be shown as follows;-

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Internal reflection

When a ray passes from one medium to another which is more optically dense, there will always be reflection and refraction for all angles.

However, when light passes in small angles of incidence from a more optically dense to a less optically dense medium. These is a strong refracted ray and a weak ray that is reflected back into the denser medium and If the angles of incidence in the denser medium is increased. The angle of refraction also increased in the less dense medium. This continuous until an angle called the critical angles is reached.

The critical angle

When an angle of incidence reaches a certain value, the angle of refraction in the less dense medium because 900. This angle of incidence is called the critical angle and it is in the denser medium.

Definition of critical angle

Critical angle [c] is the angle of incidence in the cleanser medium of which the angle of reflection in the less dense medium is 900 .

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When the angle of incidence in the denser medium exceeds the critical angles the refracted ray disappears and all the incident light is reflected back inside the denser medium. This is called total internal refraction


Total internal refraction takes place in the denser medium and occurs when the angle of incidence in the denser medium is greater than the critical angle.

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Critical angle and refractive index



Total internal reflection is used in the following ways;-



prisms 1


The critical angle for glass is 420 hence a ray that is incident on the interference at 450 is totally internally refracted.

Right angled insoles prisms can be used to reflect light through 90o as in [a] or 1800 as in [b].

Such prisms are used to replace mirrors in binoculars, microscopes, telescopes or periscopes.


A mirage is often seen as a pool of water on the road some distance a head during a hot day. As the ray moves through cool, wrong and hot air towards the earth. It is continuously refracted away from the normal until such a point when it totally reflected at a point close to the surface of the sun. The image of the sky then appears like a pool of water on the road surface to observe as shown in the diagram above.

fish eye


Due to total internal reflection that happens at the surface of water, a fish can fee object above and below the water surface.

The angle of clarity is 980 i.e. twice the critical angle. The fish can see all objects with in a cone of angle of 980 clearly if the water is clean and calm.

Optical fiber

fish eye view

Optical fibers’ consist of plastic or glass fibers’, light or laser beam that is shown into and optical fiber. An optical fiber is bounces from one ego to another by total internal reflection. This transports the beam over large distances with very little loss in intensity.

Optical fibers’ allow the beam to be carried along bends. Doctors use the fibers’ in order to see inside the human body that is otherwise inaccessible to direct light. The instrument is called an endoscope.

Optical fibers are also used in communication systems to transmit information.

Total internal reflection of radio waves by the ionosphere


Both light waves and radio waves are electromagnetic that contain electric and magnetic fields. Radio waves are reflected just like light rays. Radio waves from station T on the earth surface are beamed towards the ionosphere i.e. the region of ionized gases found at very large attitudes. As the practical density of the ionosphere decreases the waves are gradually refracted away from the normal until such a height when the waves are totally internally refracted. In this way the radio Wace can be received at location R on the other side of the earth.

Refraction of monochromatic light by a glass prism

prism 2

A is angle of prism

i is angle of incidence

e is angle f emergence

r1 and r2 are angles of refractions

d is the angle of deviation

NB: The refracted ray always directed the base of the prism.

prism 3






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