When a shell of a hollow sphere of glass is made out of a piece of glass and then silvered, a curved or spherical mirror is obtained. These mirrors due to their curvature form images that are quite different from plane mirrors.
If the glass is silvered from outside so that light can be reflected from inside, it is called concave or converging mirror.
If the coating is done so that the reflection is from outside, it is called convex or diverging mirror.
ESSENTIAL PARTS OF CURVED MIRROR
The essential parts of spherical mirrors are the aperture, the plow, the centre of curvature, the radius of curvature.
The aperture is the width (AB) of the mirror. The pole (P) is the centre of the reflecting surface of the curved mirror. The centre of curvature (c) is the centre of the sphere of which the mirror forms a part.
The radius of curvature is the distance from the pole to the centre of curvature (cp). It is the radius of curvature that determines the action of a curved mirror. For concave mirror, the radius of curvature is in front while it is behind for convex mirror.
The principal axis is the parallel line (pc) from the pole to the centre of curvature. When a beam of light is incident on a curved mirror, the rays are reflected or diverge from a point
called a focus.
The principal focus of a concave mirror is the point where rays that are parallel and close to the principal axis converge after reflection.
The principal focus of a convex mirror is the point from which rays parallel and close to the principal axis appear to diverge after reflection.
Hence, the focus of a concave mirror is real since the converging rays can be seen on the screen but of convex mirror is virtual. The focal length, f, of a spherical mirror is half of its radius of curvature.
r = 2f or f = r/2
r= radius of curvature f = focal length
FORMATION OF IMAGES BY SPHERICAL MIRROR
The position and nature of images formed by curved mirrors can be investigated by placing a brightly lit object and a screen in front of the mirror so that the light from the object is incident on the mid-point of the mirror.
RULES FOR CONSTRUCTING IMAGES FORMED BY SPHERICAL MIRROR
Rays diagrams can be constructed for images formed by spherical mirror based on the following rules:
- Rays parallel to the principal axis passes through the principal focus after reflection
- Rays through the principal focus are reflected parallel to the principal axis
- Rays passing the centre of curvature are reflected back along their path. This is in line with the principle of reversibility of light. Thus an object and its image can be interchanged. The two positions of the object and its image are called conjugate foci since an object placed at any of these positions will produce an image at the other.
(a) OBJECT AT INFINITY
The image is
- At F
- Smaller than object
(1) OBJECT BETWEEN F AND P
- The image is behind the mirror
- Larger than the object
(b) OBJECT BEYOND C
The image is
- Between C and F
- Smaller than object
(c) OBJECT AT C
The image is
- At c
- Same size as the object
(d) OBJECT BETWEEN F AND C
The image is
- Beyond C
- Larger than object
(e) OBJECT AT F
(1) the image is at infinity
IMAGE FORMED BY CONVEX MIRROR
Whatever the position of the object in a convex mirror, virtual images which are always erect and smaller than the object are formed.
APPLICATION OF THE REFLECTION OF LIGHT
Concave mirrors are used in torches, as shaving mirror, in car headlamp and in reflecting telescope. Convex mirrors are used as driving mirrors because they give erect image and have a wide field of view than a plane mirror of the same diameter.
MIRROR FORMULAE, MAGNIFICATION:
USES OF CURVED MIRROR
Concave mirrors are used as shaving mirror, as reflectors in reflecting telescopes and microscope
Reflection On Curved Mirror Practice problems
1. A concave mirror of radius of curvature 20cm produced an inverted image 3 times the size of an object placed on and perpendicular to the axis, calculate the position of the object and image.
2. A concave mirror of radius of curvature 20cm has a pin placed at 15cm from the pole. What will be the magnification of the image formed?
1. A body is projected from the ground at an angle of θ to the horizontal with a velocity of 30m/s. It reaches a maximum height of 11.25m, calculate
a. The value of θ
b. the time taken to strike the ground
c. the range
d. its velocity 2sec after projection [g= 10m/s2]
2. A ray of light is incident on a plane mirror at an angle of 35о. What is the angle made by the reflected ray with the surface of the mirror?
- The image obtain on the screen of a pin-hole camera becomes less sharply defined when the (a) object is moved further from pin-hole (b) screen is moved further from the screen hole (c) object is made smaller (d) pin-hole is made larger
2. An object 3.0m high is placed at 7.5m from a pin-hole camera. If the image is 6.0cm. What
is the distance of the film from the pin hole (a) 3.75cm (b) 7.50cm (c) 15cm (d) 30.0cm
- If the size of the hole of a pin-hole camera is increased the image formed becomes
(a) brighter and blurred (b)brighter and larger (c)brighter and sharper (d)blurred and larger
- A body that produces its own light is said to be (a) luminous (b)non- incandescent (c) opaque (d) translucent
5 A man at the back of a crowd watches a parade by holding a plane mirror just above his head the parade passes 6m behind his head and the mirror is 0.25m in front of the man how far does the image in the mirror appear to be from the man?
(a) 6.50m (b) 6. 25m (c) 6.00m (d)5.75m
Draw the position and nature of the image produced by an object placed at the following points on the concave mirror
1 Between F and P
2 At F
3 At C
4 Between F and C
5 Beyond C
6 At infinity
New school physics for senior sec pages 288-293