Spherical Mirrors
A Spherical mirror is a mirror which has the shape of a piece cut out of a spherical glass surface. The surface on which silvering is done is called the silvered surface and the reflection of light takes place from the other surface which is called the reflecting surface.
\(\stackrel\frown{AC}\) part of hollow sphere makes convex mirror and \(\stackrel\frown{BD}\) part of hollow sphere makes a concave mirror
Concave mirror is made by silvering the outer surface of the hollow sphere such that reflection takes place from the hollow or concave surface.
Convex mirror is made by silvering the inner surface such that reflection takes place from outer or bulged surface.
| Pole | The geometric center of the spherical surface of the mirror. It is represented by P. |
| Centre of curvature | The center of curvature of the mirror is the center of the sphere of which the mirror is a part. It is represented by C. |
| Radius of curvature | It is the radius of the sphere of which the mirror is a part. It is represented by R. |
| Principal axis | Straight-line joining the pole and the center of curvature. The line PC in the figure below represents the principal axis. It may extend on either side of the pole. |
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Let us now understand how the light rays are reflected from the concave and convex mirror.
Both mirrors reflect the light following the laws of reflection,i.e. angle of incidence(i) is equal to the angle of reflection(r).
When rays of light fall on a spherical mirror parallel to the principal axis, the rays are reflected following laws of reflection, \(\angle i = \angle r\). The normal at the point of incidence is obtained by joining this point to the center of curvature C. The reflected rays in the case of the concave mirror meet at point F on the principal axis. This point is called the focus of the concave mirror. In the case of a convex mirror, the reflected rays do not meet at any point, but they appear to come from a point F on the principal axis, this point is called the focus of the convex mirror. Focus is represented by the letter F.
Focal length: the distance of the focus from the pole of the mirror is called the focal length of the mirror. The focal length in the above figure is distance PF.
f = PF
Focal length (f) is half the radius of curvature.
\(f = \frac{1} {2}R\)
IMAGES FORMED BY SPHERICAL MIRROR
To construct the image of an object due to reflection by a spherical mirror consider three rays:
1) Ray parallel to the principal axis, after reflection, passes through the focus in case of a concave mirror or appears to come from the focus in case of a convex mirror.
2) Ray passing through the center of curvature is incident normally on the spherical mirror, therefore the rays get reflected back along its own path.
3) Ray passing through focus in case of a concave mirror or appears to pass through the focus in case of the convex mirror gets reflected parallel to the principal axis.
Real and Virtual image: A real image is formed when the reflected rays actually meet at a point. It is inverted and can be obtained on the screen. A Virtual image is formed when reflected rays meet on producing them backwards. It is erect and cannot be obtained on the screen.
| Ray Diagram | Specification |
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Position of the object: At infinity Position of the image: At focus(F) Nature of the image: Real, inverted and diminished |
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Position of the object: Beyond the center of curvature(C) Position of the image: Between focus(F) and the center of curvature(C) Nature of the image: Real, inverted and smaller than the object |
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Position of the object: At the center of curvature(C) Position of the image: At the center of curvature(C) Nature of the image: Real inverted and of same size |
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Position of the object: Between the center of curvature(C) and focus(F) Position of the image: Beyond the center of curvature(C) Nature of the image: Real, inverted and bigger than the object |
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Position of the object: At the focus(F) Position of the image: Infinity Nature of the image: Real, inverted and highly magnified |
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Position of the object: Between the focus(F) and pole(P) Position of the image: Behind the mirror Nature of the image: Virtual, erect and enlarged
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| Ray diagram | Specification |
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Position of the object: At infinity Position of the image: At focus Nature of the image: Diminished to a point, virtual and upright |
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Position of the object: At any other point Position of the image: Between focus and pole Nature of the image: Diminished, virtual and upright
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1. To find the focus of the concave mirror:
Take a concave mirror and hold it such that it faces the sun. Now place a piece of paper in front of it and adjust its distance from the mirror such that a very small image of the sun is seen on the paper. Keep it for some time and you will notice that paper chars at this point. This point is the focus of the concave mirror.
2. Take a polished steel spoon. The inside surface of the spoon is curved inwards and has a concave shape while the outside surface is curved outwards and has a convex shape. Hold the spoon such that the inside surface is facing towards you. Now move the spoon away from you, and you will notice that the image becomes inverted. This shows the image formation in a concave mirror. Now hold the spoon with the outside surface towards your face. Now observe the image. You will observe that image is erect but diminished and when you move the spoon away from you the image remains diminished and erect. This shows the image formation in a convex mirror.
