Light - Reflection and Refraction

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• Summary

The reflecting surface of a spherical mirror may be curved inwards or outwards. A spherical mirror is that mirror whose reflecting surface is the part of a hollow sphere of glass.

The spherical mirrors are of two types: Concave mirror and Convex mirror.

Concave: A concave mirror is that spherical mirror in which the reflection of light takes place at the concave surface (or bent-in surface).

Convex: A convex mirror is that spherical mirror in which the reflection of light takes place at the convex surface (or bulging –out surface).

Centre of Curvature(C): The centre of curvature of a spherical mirror is the centre of the hollow sphere of a glass of which the spherical mirror is a part. It is represented by letter ‘C’.

Pole(P): The pole of a spherical mirror is the centre of the mirror. It is represented by letter ‘P’.

The radius of Curvature(R): The radius of curvature of a spherical mirror is the radius of the hollow sphere of a glass of which the spherical is a part. It is represented by the letter ‘R’.

Principal axis: The principal axis of a spherical mirror is the straight line passing through the centre of curvature C and pole P of the spherical mirror, produced on both sides.

Aperture: The aperture of a spherical mirror is the diameter of the reflecting surface of the mirror.

Focal Length: The focal length of a spherical mirror is the distance between its pole and principal focus. It is denoted by the letter ‘f’.

The relation between Radius of curvature and focal length of a spherical mirror.The focal length of a spherical mirror is equal to half of its radius of curvature.
F = R/2R
R = 2F

Magnification of Spherical Mirrors

It is the ratio of the height of the image to the height of the object.

m = height of image/height of Object

wiris equation require

If ‘m’ is negative, the image is real.
If ‘m’ is positive, the image is virtual.
If hi = ho then m = 1, i.e., image is equal to object.
If hi > hi then m > 1 i.e., image is enlarged.
If hi < ho then m < 1 i.e., the image is diminished.

Magnification of plane mirror is always + 1.

‘+’ sign indicates virtual image.

‘1’ indicates that image is equal to object’s size.

1. If ‘m’ is ‘+ve’ and less than 1, it is a convex mirror.
2. If ‘m’ is ‘+ve’ and more than 1, it is a concave mirror.
3. If ‘m’ is ‘-ve’, it is a concave mirror.

Rules for making ray diagrams by the concave mirror

1. A ray parallel to the principal axis will pass through the principal focus, after reflection.
2. A ray passing through the principal focus of concave mirror will emerge parallel to principal axis after reflection.
3. A ray of light passing through the centre of curvature of a concave mirror is reflected back along the same path as it is a normally incident ray.
4. A ray incident obliquely to the principal axis of a concave mirror is reflected obliquely making an equal angle.

Sign Convention for Reflection by Spherical Mirror or New Cartesian Sign Convention

1. The object is placed to the left of the mirror.
2. All distances parallel to the principal axis are measured from the pole of the mirror.
3. All distances measured in the direction of incident ray (along with + X-axis) are taken as positive and those measured against the direction of incident ray (along – X-axis) are taken as negative.
4. Distance measured perpendicular to and above the principal axis are taken as positive.
5. Distances measured perpendicular to and below the principal axis are taken as negative.

Object distance = ‘u’ is always negative

Focal length of concave mirror = Negative

Focal length of convex mirror = Positive

Mirror Formula :

where,
v = Image distance
u = Object distance
f = Focal length

Magnification of Spherical Mirrors

It is the ratio of the height of the image to the height of the object.

m = height of image/height of Object

wiris equation require

If ‘m’ is negative, the image is real.
If ‘m’ is positive, the image is virtual.
If hi = ho then m = 1, i.e., image is equal to object.
If hi > hi then m > 1 i.e., image is enlarged.
If hi < ho then m < 1 i.e., the image is diminished.

Magnification of plane mirror is always + 1.

‘+’ sign indicates virtual image.

‘1’ indicates that image is equal to object’s size.

1. If ‘m’ is ‘+ve’ and less than 1, it is a convex mirror.
2. If ‘m’ is ‘+ve’ and more than 1, it is a concave mirror.
3. If ‘m’ is ‘-ve’, it is a concave mirror.