lecture 11 a reflection by lmUp4Z0f




Light is a form of energy which travels in a vacuum at a
speed of 3 x 108 m.s-1 Light can exhibit properties of both
waves and particles (photons). This property is referred to as
wave–particle duality. The study of light, known as optics, is
an important area in physics.
Substances which allow light to pass through them are called
transparent materials and substances which prevent light
passing through are called opaque.

Light travels in straight lines which can be demonstrated by
placing three cardboards A, B and C and make a pinhole at
their centres. Place a burning candle on one side of the
cardboard A and arrange the cardboards in such a way that
the three pinholes and the candle flame are in a straight line.
The candle flame will be visible through the pinhole of the
cardboard C. If any one of the cardboards is slightly
displaced the flame will not be visible. From this it is clear
that light travels in a straight line.

The light can be seen by the observer at O if and only if A, B
and C are in a straight line.
Also through one pinhole the image is formed by the light
travelling in straight lines and is inverted

A ray of light is the direction of the path taken by the light
A beam is a stream of light energy or a collection of rays.

A beam can be
1. Parallel

A collection of parallel rays

2. Diverging

A collection of rays diverging from a point.
3. Converging.

A collection of rays converging to a point.


When light falls on a smooth highly polished surface it is
reflected i.e turned back. A piece of polished metal makes a
good reflector.


LAW 1. The incident ray, the reflected ray and the normal
all lie in the same plane.

Normal is the direction at 90o to the direction of the surface at
the point.

LAW 2. The angle of incidence equals the angle of
reflection. Both angles measured relative to the normal.
Example : Plane Mirror. Glass mirrors have a thin layer of
silvering deposited on the back of the glass which is
protected. An IMAGE is produced in the mirror. The term
image is used for any reproduction of an object by means of
rays of light.

The image in a plane mirror is always

  1 Same size as the object and the same way up

2. As far behind the mirror as the object is in front.

3. Turned sideways or laterally inverted

4. In the case of plane mirrors, the image is said to be a
   virtual image. Virtual images are images which are
   formed in locations where light does not actually reach.
   Light does not actually pass through the location on the
   other side of the mirror; it only appears to an observer as
   though the light is coming from this location.

   Note an alternative description is that
   A real image can be focused on a screen, whereas a
   virtual image can not.
The angle of incidence i is the angle between the incident ray
and the normal.

The reflected ray r is the angle between the reflected ray and
the normal.

The angle of incidence i is equal to the angle or reflection r

                        i  r
Locating an Image in a plane mirror

Take a point object O the image is also a point I
To identify one particular point you need two lines.
Therefore to locate a point we will use the intersection of two
reflected rays. From the point O produce two incident rays.
Each incident ray has a reflected ray

The intersection of the reflected rays indicates the location of
the image.
In the case of the plane mirror we notice that the reflected
beam produced is a diverging beam and that the rays
APPEAR to be diverging from a point behind the mirror.

The distance from M to O = the distance from M to I
The reflected rays form a diverging beam which APPEAR to
come from I

In a plane mirror we can see that

  1. Image is same size as the object the same way up and
    the same distance behind the mirror as the image is in
2. Laterally inverted

3. Virtual Image
     Curved Reflectors.

Curved Mirrors are parts of spherical surfaces.

There are two types

     1.   Concave or Converging Mirrors

     2. Convex or Diverging Mirrors

The mirror is part of a sphere of centre c known as the centre
of curvature of the mirror.

The middle point p of the mirror is known as the pole of the

The mirror is symmetrical about the line pc which is called
the PRINCIPAL AXIS. The radius of the sphere of which the
mirror is part i.e. PC = r and is known as the radius of

The width of the mirror ST is known as the aperature.
        Concave Mirror

Convex Mirror
It can be shown that a parallel beam of light incident on a
concave mirror is reflected to a converging beam that
passes through a point F on the principal axis known as
the principal focus.

In a concave mirror the rays reflected by the mirror
actually pass through F and it is called a real focus.

The distance from F to the pole of the mirror P is called
the focal length of the mirror, f

F P = f

Any incident ray parallel to the principal axis is reflected
so as to pass through the principal focus F.
   In a convex mirror when a parallel beam is incident on
   the mirror the reflected rays form a divergent beam.
   However when produced back all the rays seem to come
   from one point F behind the mirror.

   The rays only appear to come from F and it is said to be a
   virtual focus.


   F P = f focal length

For both mirrors

F P =       f     focal length

 C P    =       r radius of curvature

It can be shown that        f 
If the object in a curved reflector is a point O then we find
the point of the image by the point of intersection of two
reflected rays.

There is a set of rules to follow when finding rays

1. Rays incident at the pole are reflected making the same
   angle with the principal axis.

2. Rays passing through the centre of curvature are reflected
   back along their own path.

3. Rays parallel to principal axis are reflected through the
   principal focus.

4. Rays through the principal focus are reflected parallel to
   the principal axis.
  1. A REAL image is formed by the actual intersection of
     reflected rays.

   2. A VIRTUAL image is one formed by the apparent
   intersection of reflected rays when their directions have
   been produced backwards.

3. The principle of reversibility states that light will follow
   exactly the same path if its direction of travel is reversed.
   If a light ray travels from A to B along a path it will travel
   from B to A back along the same path in the reverse

4. The direction joining any point on the mirror to the point
   c (the center of curvature ) is the Normal to the mirror at
   that point.

5. All angles are measured relative to the Normal.

Using the above rules we may now easily find the images
formed by a concave mirror.
For each image formed we need to determine

     (i)     Its location relative to the mirror.
     (ii)    Whether it is real or virtual.
     (iii)   Whether it is upright or inverted.
     (iv)    Its size relative to the object.

The chosen object is a vertical line with two points (e.g.
arrow or candle) To locate the image of the object we must
locate the image of both the bottom and the top point. The
bottom of the arrow is placed along the principal axis so that
its image is always at some point along the principal axis.
The image of the top point is located by the intersection of
two reflected rays. The two image points are joined together
to produce the image.
  1. Object between F and P

Image is
  (i) Behind the mirror
  (ii)    Virtual
  (iii) Upright
  (iv)    Larger than the object.

  2. Object at F

Image is at infinity
  3. Object between F and C

Image is
  (i) Beyond C
  (ii)    Real
  (iii) Inverted
  (iv)    Larger than object

  4. Object at C

Image is
    (i)     At C
    (ii)    Real
    (iii)   Inverted
    (iv)    Same size as object
  5. Object beyond C

Image is

    (i)     Between F and C
    (ii)    Real
    (iii)   Inverted
    (iv)    Smaller than object

  6. Object at infinity


    (i)     At F
    (ii)    Real
    (iii)   Inverted
    (iv)    Smaller than object
Images in a convex mirror

Experiments show that the image formed in a convex mirror
is always

     (i) Virtual
     (ii) Upright
     (iii) Smaller than object

Regardless of where the object is located.

Therefore If the image is REAL the mirror is CONCAVE

If the image is VIRTUAL the mirror is

Summary Mirrors         Concave
a)Distant                                       Inverted
object                                          Smaller than object
                                                At F

b) Object                                       Inverted
beyond C                                        Smaller
                                                Between C and F

c) Object at C
                                                Same size as object
                                                At C

d) Object                                       Inverted
between C                                       Larger
and F                                           Beyond C

e) Object
between F                                       Virtual
and P                                           Erect
                                                Larger than object
                                                Behind mirror

                                                No image
f) Object at F                                  Reflected rays
                                                are parallel

Images formed by a diverging spherical mirror
                                                regardless of object
                                                position IMAGE IS
                                                Smaller than object
                                                      Behind mirror between
                                                      F and P

                MIRROR EQUATION
All distance values are measured with the mirror as the origin
i.e. the pole P We use the following symbols

u = distance from the object to the mirror

v = distance from the image to the mirror

f = focal length distance from focus to mirror

For a spherical mirror it can be proved that

                          1 1 1
                            
                          u v f

and also that the magnification m

                        height of image v
                   m                   
                        height of object u

A convention that we can use for mirrors is the REAL IS
POSITIVE convention
It is that any distance from a real object is taken as a positive
value and any virtual distance is given a negative value.
REAL +VE             AND VIRTUAL _-VE

Concave mirror Real focus so f is +ve
Convex mirror Virtual focus so f is –ve

Question 1. A concave mirror has a radius of curvature of 40
cm. A real object 5 cm high is placed 30 cm in front of the
mirror (i)calculate the position and height of the image. Is the
image real or virtual? (ii) locate the image using ray tracing
(iii) repeat the calculations if the object is placed 60 cm from
the mirror (ii) repeat for a convex mirror.

Question 2. An object is placed 25 cm from a concave mirror
of radius 80 cm. (i) Determine the position relative size and
type of image that is produced (ii) repeat for a convex mirror
(iii) show the ray tracing

Question 3. (i) What type of mirror should be used in order
to give an erect image 1/5 th the size of an object placed 15
cm in front of it? (ii) calculate the focal length of the mirror.

Question 4. It is desired to cast the image of a lamp
magnified 5 times upon a wall 12 m from the lamp. What
kind of mirror is required and what is its focal length ?

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