Reflection of Light by Curved or Spherical Mirrors
Apart from plane mirrors, curved mirrors also reflect light incident on them. Curved mirrors form
parts of the surface of spheres. Such mirrors are therefore called spherical mirrors, and they have a large
number of scientific and practical applications. Shaving mirrors, car driving mirrors, parabolic mirrors of
telescopes, mirror reflectors of searchlights are such applications.
There are two (2) types of curved mirrors –
i.
ii.
Concave (or converging mirror)
The outside surface is silvered and the inside surface is the reflecting part.
Convex (or diverging) mirror
the inner surface is silvered and the outer surface is the reflecting part.
The essential parts of spherical mirrors are:





Note:
Aperture – is the width of the mirror.
Pole (P) – is the centre of the reflecting surface of the curved mirror.
Centre of curvature (C) – is the centre of the sphere of which the mirror forms a part.
Radius of curvature (r) – is the radius of the sphere of which the mirror forms a part.
Principal axis – is the line from the pole to the centre of curvature.
When parallel rays of light close to and parallel to the principal axis are incident on a
concave mirror, they converge or come together after reflection to a point F on the principal
axis called the principal focus. By contrast, when such rays are incident on a convex mirror,
they diverge from the surface and appear to come from the point F on the principal axis
behind the mirror.
The principal focus (F) of a curved mirror is that point on the principal axis to which
incident rays parallel and close to the ptincipal axis converge or from which they appear to
diverge after reflection.
The principal focus of a concave mirror is said to be real focus because the reflected rays actually pass
through it. This point of convergence can actually be obtained on a screen placed in front of the mirror as a
bright spot of light. On the contrary the principal focus of a convex mirror is a virtial focusas the reflected
rays do not actually pass through it. If a screen is placed behind a convex mirror, no bright spot of light or
image of an object is seen on the screen.
The focal length (f) of a curved mirror in each case is the distance from the principal focus to the pole.It is
found, experimentally and also by the geometry of the mirror, to be equal to half the radius of curvaturefor
both types of mirrors.
𝑓𝑜𝑐𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ, 𝑓 =
𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑐𝑢𝑟𝑣𝑎𝑡𝑢𝑟𝑒 (𝑟)
2
Thus the principal focus (F) is midway between the pole (P) and the centre of curvature (C).
 Formation of images by Curved Mirrors
The size, nature and position of an image formed by a curved mirror depends on the position
of the object from the pole of the mirror.
The ray diagrams of images in concave mirrors
The following rules must be followed in order to understand the diagrams below;
1. A ray parallel and close to the principal axis passes through the principal focus (F) after reflection.
2. A ray through the centre of curvature, strikes the mirror normally and is reflected back along the
same line or path.
3. As a corollary to (1) any ray from the object which passes through the principal focus strikes the
mirror and is reflected parallel to the principal axis.

When the object is beyond the centre of curvature, beyond 2f or > 2𝑓

When the object is at the centre of curvature or 2f

When the object is between the principal focus and the centre of curvature or < 2𝑓

When the object is at the principal focus

When the object is between the principal focus and the pole
Note : This is the only situation when a concave mirror produced a virtual image.
A convex mirrorforms only virtual, erectand diminished images. The image is formed at the intersection
of the reflected rays produced backwards (in broken lines) and is formed behind the mirror. This is the case
for all positions of the objects in front of the mirror.
Experimental Determination of the focal length of curved mirrors
i.
ii.
iii.
iv.
Quick but approximate method;
Focal length from measurement of the radius of curvature;
By the use of search pin and the method of no parallax;
By the use of the mirror equation.
𝟏 𝟏 𝟏
+ =
𝒖 𝒗 𝒇
Where u --- object distance
v --- image distance
f ---focal length
𝟏
𝟏
𝟏
Note : The intercept on either axis of a graph of𝒖against 𝒗is equal to equal to 𝒇. The reciprocal of this
intercept gives the value of the focal length.
Sign convection
When the mirror formula is used in solving practical problrms, it is necessary to add a positive (+) or
a negative (-) sign to each of the distances according to the sign rule given below.




Real objects and real images are to be considered a positive distance from the mirror.
Virtual images are at a negative distance from the mirror.
Focal length of a concave mirror is positive.
Focal length of a convex mirror is negative.
𝒗
Linear Magnification (m) produced by a mirror is given by 𝒎 = 𝒖 =
𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒊𝒎𝒂𝒈𝒆
𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒐𝒃𝒋𝒆𝒄𝒕
.
Practical applications of Curved mirrors

Concave mirrors are used as shaving mirrors because when a man places his face near the mirror
(i.e. between the principal focus and the pole), he sees an enlarge, erect and virtual image of the
face.
It is also used by the Dentist for the same reason mentioned above.


Concave mirrors are used as reflectors in reflecting telescope and microscopes.
Convex mirrors are used as driving mirrors of motor carsbecause they give erect imageof an
object behind the driver. In addition, such convex mirrorsprovide a wide field of view. Therefore,
objectswithin a large angle can be seen with the help of the mirror.
Convex mirror has some disadvantages when used as driving mirror. These are
i.
The image is always smaller than the object.
ii.
It gives a false impression of the distance as image seems further away.

Use of parabolic mirrors in car headlamps and searchlight.
A parabolic mirror is a special type of concave mirrorwhich has the shape of a parabola.
The parabolic mirror produces a wide parallel beam of light of constant intensity when a
small light source is placed at its focus.
Parabolic mirrorsare used in car headlamps and as searchlights. Spherical concave
mirrors are not used in these devices because they do not provide a parallel beam of
constant intensity.
Further notes on the number of images, n formed by two plane mirrors inclined at angle 𝜃

If
n=

If
n=

If
n=

If
360
= 𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟
𝜃
360
𝜃
360
= 𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑜𝑏𝑗𝑒𝑐𝑡 𝑙𝑖𝑒𝑠 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝑎𝑙𝑙𝑦
𝜃
360
𝜃
360
−1
−1
= 𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑜𝑏𝑗𝑒𝑐𝑡 𝑙𝑖𝑒𝑠 𝑎𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝑎𝑙𝑙𝑦
𝜃
360
𝜃
360
𝜃
= 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛
n = only integer part of If
360
𝜃