Notes On Spherical Mirror - CBSE Class 7 Science

Mirrors are the basic means of viewing our own beauty. There are two types of mirrors – plane mirrors and curved mirrors. If the curved mirror is a part of a huge sphere, then the mirror is a spherical mirror. Spherical mirrors can be further classified into two types – concave mirrors and convex mirrors.  Like plane mirrors, spherical mirrors also follow the laws of reflection. 

Terms Associated with Spherical Mirrors

     •  Centre of curvature (C) is the centre of the sphere, of which the mirror is a part.
     •  Radius of curvature (R) is the radius of the sphere, of which the mirror is a part.
     •  Pole (P) is the geometric centre of the spherical mirror.
     •  Principal axis is the line joining the pole and the centre of curvature.
     •  Principal focus (F) is the point on the principal axis, where a parallel beam of light, parallel to the principal axis after reflection converges in the case of a concave mirror and appears to diverge from in the case of a convex mirror.
     •  Focal length (f) is the distance of the principal focus from the pole of the mirror.

There are two types of images: real and virtual. Real images are those that can be caught on a screen while virtual images are those that cannot be caught on a screen.

Concave Mirror

If a part of a hollow glass sphere is cut and the cut part of the sphere is coated outside with silver or similar material, then its inner surface reflects the entire light incident on it, and thus, forms a mirror. Since the inner surface is a concave surface, the mirror so formed is called a concave mirror.

Concave mirrors converge the light incident on them and hence are called converging mirrors. You can observe yourself magnified when the mirror is placed close to your face. This is due the position of the object between the focus and the pole. As the object moves away from the mirror, the size of its image reduces along with its distance from the mirror. If an object is placed close to a concave mirror such that the distance between the mirror and the object is less than its focal length, then a magnified and virtual image is formed. Due to this property, concave mirrors are used as shaving mirrors, and by dentists to view clearly the inner parts of the mouth.

Convex Mirror

If the cut part of the glass sphere is coated from inside with silver or a similar material, then its outer surface reflects the entire light incident on it, and thus forms a mirror. Since the outer surface is a convex surface, the mirror so formed is called a convex mirror.

Convex mirrors diverge the light incident on them and hence they are called the diverging mirrors. Due to this they always form diminished, virtual and erect images irrespective of the position of the object in front of them. Thus, the magnification produced by these mirrors is always less than one. The field of view for a convex mirror is greater than that for a plane mirror, the aperture being the same. Hence, convex mirrors are used as rear-view mirrors in vehicles. It is also installed behind automated teller machines as a security measure. 

Mirror Formula and Sign Conventions 

The relation between the focal length (f), object distance (u) and the image distance (v) is given by 1 f = 1 u + 1 v . This is called the mirror formula.

All the distances are measured from the pole of the mirror. If we measure the distances in the direction of the incident light, then they are taken positive or else they are taken negative. These constitute the sign conventions.

Summary

Mirrors are the basic means of viewing our own beauty. There are two types of mirrors – plane mirrors and curved mirrors. If the curved mirror is a part of a huge sphere, then the mirror is a spherical mirror. Spherical mirrors can be further classified into two types – concave mirrors and convex mirrors.  Like plane mirrors, spherical mirrors also follow the laws of reflection. 

Terms Associated with Spherical Mirrors

     •  Centre of curvature (C) is the centre of the sphere, of which the mirror is a part.
     •  Radius of curvature (R) is the radius of the sphere, of which the mirror is a part.
     •  Pole (P) is the geometric centre of the spherical mirror.
     •  Principal axis is the line joining the pole and the centre of curvature.
     •  Principal focus (F) is the point on the principal axis, where a parallel beam of light, parallel to the principal axis after reflection converges in the case of a concave mirror and appears to diverge from in the case of a convex mirror.
     •  Focal length (f) is the distance of the principal focus from the pole of the mirror.

There are two types of images: real and virtual. Real images are those that can be caught on a screen while virtual images are those that cannot be caught on a screen.

Concave Mirror

If a part of a hollow glass sphere is cut and the cut part of the sphere is coated outside with silver or similar material, then its inner surface reflects the entire light incident on it, and thus, forms a mirror. Since the inner surface is a concave surface, the mirror so formed is called a concave mirror.

Concave mirrors converge the light incident on them and hence are called converging mirrors. You can observe yourself magnified when the mirror is placed close to your face. This is due the position of the object between the focus and the pole. As the object moves away from the mirror, the size of its image reduces along with its distance from the mirror. If an object is placed close to a concave mirror such that the distance between the mirror and the object is less than its focal length, then a magnified and virtual image is formed. Due to this property, concave mirrors are used as shaving mirrors, and by dentists to view clearly the inner parts of the mouth.

Convex Mirror

If the cut part of the glass sphere is coated from inside with silver or a similar material, then its outer surface reflects the entire light incident on it, and thus forms a mirror. Since the outer surface is a convex surface, the mirror so formed is called a convex mirror.

Convex mirrors diverge the light incident on them and hence they are called the diverging mirrors. Due to this they always form diminished, virtual and erect images irrespective of the position of the object in front of them. Thus, the magnification produced by these mirrors is always less than one. The field of view for a convex mirror is greater than that for a plane mirror, the aperture being the same. Hence, convex mirrors are used as rear-view mirrors in vehicles. It is also installed behind automated teller machines as a security measure. 

Mirror Formula and Sign Conventions 

The relation between the focal length (f), object distance (u) and the image distance (v) is given by 1 f = 1 u + 1 v . This is called the mirror formula.

All the distances are measured from the pole of the mirror. If we measure the distances in the direction of the incident light, then they are taken positive or else they are taken negative. These constitute the sign conventions.

Videos

Activities



Activity 1

micro.magnet.fsu.edu has developed an interactive tutorial which explores how moving the object farther away from the center of curvature of a concave mirror affects the size of the real image formed by the mirror. This shows that an object placed beyond the center of curvature of a concave mirror forms a real and inverted image between the focal point and the center of curvature. There is an Object Position slider to move the object (owl) back and forth in front of the mirror. As the object approaches the mirror, the inverted, real image grows larger, approaching the size of the object, but becomes much smaller as the object is moved farther away from the center of curvature.

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Activity 2

nd.edu/~ysun/Yang has created an interactive activity which shows the images formed by a concave mirror for various positions of an object  (candle). By clicking the candle positioned at five different places one observes that the image formed by a concave mirror can be either real-inverted or virtual-erect. The size of the image also varies depending on the position of the object.

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Activity 3

micro.magnet.fsu.edu has developed an interactive java tutorial which explores how moving the object farther away from a convex mirror's surface affects the size of the virtual image formed behind the mirror. It shows that the image formed by a convex mirror is always virtual, erect and diminished, irrespective of the position of the object. There is an Object Position slider to move the object (owl) back and forth in front of the mirror. As the object approaches the mirror, the erect, real image grows larger, approaching the size of the object, but becomes much smaller as the object is moved farther away from the reflecting surface of the mirror.

Go to Acivity


Activity 4

nd.edu/~ysun/Yang has created an interactive activity which shows the images formed by a convex mirror for various positions of an object  (candle). By clicking the candle positioned at three different places one observes that the image formed by a convex mirror is always virtual, erect and diminished, irrespective of the position of the object.

Go to Activity


References

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