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Spherical Mirrors

A mirror whose reflecting surface is a part of a sphere is called a spherical mirror. Spherical mirrors are of two types as shown in Figure 9.5.

Concave mirror: A concave mirror is made by silvering the outer or bulging surface, such that the reflection takes place from the hollow or concave surface.

Convex mirror: A convex mirror is made by silvering the inner surface, such that the reflection takes place from the outer bulging surface as shown in Figure 9.5(b).

 

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Figure 9.5 Spherical Mirrors

 

Take a stainless steel spoon and bring the outer side of the spoon near your face and look into it. What will you observe? What do you observe if the inner side of the spoon is brought near your face?
 
In the first case you would observe an upright and enlarged image of your face while in the latter case you would observe an inverted and diminished image. Here, the curved shining surfaces of the spoon are acting as mirrors.

Terms Related to Spherical Mirrors

  1. Aperture: The surface area of the spherical mirror from which reflection takes place is called its aperture. It is denoted by MM´ as shown in Figure 9.6.
  2. Pole: The centre of the spherical mirror is called the pole. It is denoted by P (Figure 9.7).
Description: Description: 87321.png                   Description: Description: 87355.png
Figure 9.6 Concave Mirror Figure 9.7 Convex Mirror
  1. Centre of curvature: The geometric centre of the hollow sphere of which spherical mirror is a part is called the centre of curvature of the spherical mirror. It is denoted by C (see Figure 9.6 and 9.7).
  2. Radius of curvature: The radius of the hollow sphere of which the spherical mirror is a part is called the radius of curvature of the spherical mirror. It is also the distance between the pole and the centre of curvature of the spherical mirror (PC). It is denoted by R.
  3. Principal axis: The straight line passing through the centre of curvature and the pole of a spherical mirror is called its principal axis (PX).
  4. Principal focus (F): If a beam of light parallel to the principal axis is incident on a concave mirror, all the rays after reflection converge at a point on the principal axis. This point is called the principal focus (F) of the concave mirror (Figure 9.8).

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Figure 9.8 Principal Focus of a Concave Mirror (F)
 

Similarly, if a beam of light parallel to the principal axis is incident on a convex mirror, all the rays after reflection diverge. If the reflected rays are extended backwards, they appear to diverge from a point on the principal axis. This point is called the principal focus of a convex mirror (Figure 9.9).
  1. Focal length (f): The distance between the pole (P) and principal focus (F) is called the focal length (f).
     
    If ‘f’ is the focal length and ‘R’ is the radius of curvature, then
    R = 2f or f = Description: 82384.png
     
    This relation is true for a concave as well as a convex mirror.

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Figure 9.9 Principal Focus of a Convex Mirror (F)

Image Formed by a Concave Mirror

When an object is placed in front of a concave mirror, light rays from the object fall on the mirror and get reflected. The reflected rays produce an image at a point where they intersect or appear to intersect each other. For a given object, the image can be constructed by considering the following rays.
  1. A ray from the object, passing through the principal focus and falling on the concave mirror is reflected along a direction parallel to the principal axis.
  2. A ray from the object, parallel to the principal focus and falling on the concave mirror is reflected along a direction passing through the principal focus.
  3. A ray from the object, passing through the center of curvature and falling on the concave mirror, retraces its path.
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Fig. 9.10 Object at Infinity
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Fig. 9.11 Object Beyond C
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Fig. 9.12 Object at C
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Fig. 9.13 Object Between F and C
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Fig. 9.14 Object at F
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Fig. 9.15 Object Between F and P
 
Position of the Object
Position of the Image
Nature of the Image
Uses
1. At infinity (Figure 9.10)
At the focus (F)
Real, inverted and very small (diminished)
In solar cookers
2. Beyond C (Figure 9.11)
Between F and C
Real, inverted and diminished
3. At C (Figure 9.12)
At C
Real, inverted and same size of the object
As a reflecting mirror behind a projection lamp in flood lights
4. Between F and C
(Figure 9.13)
Beyond C
Real, inverted, bigger than the object (enlarged)
5. At the focus F (Figure 9.14)
At infinity
Real, inverted and enlarged
As a reflecting mirror in car head lights. Search light, torch, etc.
6. Between F and P
(Figure 9.15)
Behind the mirror
Virtual, erect and enlarged
As a shaving or make up mirror, dentists mirror, flood light, etc.

Image Formed by a Convex Mirror

The rays falling on a convex mirror after reflection diverge (Figure 9.16). Whatever may be the position of the object in front of a convex mirror, we always get the image having the following characteristics:
  1. The image is virtual and formed behind the mirror.
  2. It is always erect and diminished.

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Fig. 9.16 Image Formation by a Convex Mirror
 

Uses of a convex mirror
 
Convex mirrors are used in the following applications:
  1. Rear view mirrors of cars use convex mirrors to produce an erect and diminished image of the objects approaching from behind.
  2. Street lights also use convex mirrors to diverge light over an extended area.
  3. Convex mirrors are placed on the staircase of double-decker buses.
  4. Convex mirrors are used as vigilance mirrors in big shops and departmental stores.

Mirror Formula

Mirror formula is the relation between the focal length ‘f’ of the mirror, the distance ‘u’ of the object from the pole of the mirror and the distance ‘v’ of the image from the pole.

According to mirror formula,
 
Description: 82613.png

u and v are positive for real object and real image; u and v are negative for virtual object and virtual image. f is positive for convex mirror; f is negative for concave mirror.
 
Linear Magnification of the Mirror
 
Linear magnification is the ratio of the size of the image to the size of the object, denoted by ‘m’. Therefore,
 
Magnification Description: 82622.png
 
where hi is the height of the image and ho is the height of the object.




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