Light - Reflection and Refraction

Class 10 Science

An object reflects light that falls on it. This reflected light, when received by the eyes, enables to see things.

Reflection of Light

A highly polished surface, such as a mirror, reflects most of the light falling on it.

Laws of Reflection

  1. The angle of incidence is equal to the angle of reflection.
  2. The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane.

Image formed by a plane mirror is always virtual and erect. The size of the image is equal to that of the object. The image formed is as far behind the mirror as the object is in front of it. Further, the image is laterally inverted.

Spherical Mirrors

The reflecting surface of a spherical mirror may be curved inwards or outwards. A spherical mirror, whose reflecting surface is curved inwards, that is, faces towards the centre of the sphere, is called a concave mirror. A spherical mirror whose reflecting surface is curved outwards, is called a convex mirror.

Pole

The centre of the reflecting surface of a spherical mirror is a point called the pole. It lies on the surface of the mirror. The pole is represented by the letter P.

Centre of Curvature

The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C.

Radius of Curvature

The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror. It is represented by the letter R.

The distance PC is equal to the radius of curvature.

Principal Axis

A straight line passing through the pole and the centre of curvature of a spherical mirror is called the principal axis. Principal axis is normal to the mirror at its pole.

Focus

A number of rays parallel to the principal axis are falling on a concave mirror. The reflected rays intersect at a point on the principal axis of the mirror. This point is called the principal focus of the concave mirror.

In convex mirror, the reflected rays appear to come from a point on the principal axis. This point is called the principal focus of the convex mirror.

The principal focus is represented by the letter F.

Focal Length

The distance between the pole and the principal focus of a spherical mirror is called the focal length. It is represented by the letter f.

For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length.

R = 2f

This implies that the principal focus of a spherical mirror lies midway between the pole and centre of curvature.

Image Formation by Spherical Mirrors

The nature, position and size of the image formed by a concave mirror depends on the position of the object in relation to points P, F and C.

  1. A ray parallel to the principal axis, after reflection, will pass through the principal focus in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror.
  2. A ray passing through the principal focus of a concave mirror or a ray which is directed towards the principal focus of a convex mirror, after reflection, will emerge parallel to the principal axis.
  3. A ray passing through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path.
  4. A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror or a convex mirror, is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal angles with the principal axis.

Uses of Spherical Mirrors

Uses of concave mirrors

Concave mirrors are commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light. They are often used as shaving mirrors to see a larger image of the face. The dentists use concave mirrors to see large images of the teeth of patients. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

Uses of convex mirrors

Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles. These mirrors are fitted on the sides of the vehicle, enabling the driver to see traffic behind to facilitate safe driving. Convex mirrors are preferred because they always give an erect, though diminished, image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view much larger area than would be possible with a plane mirror.

Sign Convention for Reflection by Spherical Mirrors

The pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X) of the coordinate system.

  1. The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
  2. All distances parallel to the principal axis are measured from the pole of the mirror.
  3. All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along - x-axis) are taken as negative.
  4. Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
  5. Distances measured perpendicular to and below the principal axis (along - y-axis) are taken as negative.

Mirror Formula and Magnification

In a spherical mirror, the distance of the object from its pole is called the object distance (u). The distance of the image from the pole of the mirror is called the image distance (v). The distance of the principal focus from the pole is called the focal length (f).

$$ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} $$

Magnification

Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as the ratio of the height of the image to the height of the object.

The magnification m is also related to the object distance (u) and image distance (v).

$$ m = \frac{h'}{h} = -\,\frac{v}{u} $$

The height of the object is taken to be positive as the object is usually placed above the principal axis. The height of the image should be taken as positive for virtual images. However, it is to be taken as negative for real images. A negative sign in the value of the magnification indicates that the image is real. A positive sign in the value of the magnification indicates that the image is virtual.

Refraction of Light

When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.

Rectangular Glass Slab

Refraction is due to change in the speed of light as it enters from one transparent medium to another.

Laws of Refraction of Light

  1. The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
  2. The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction. (This is true for angle 0 < i < 90°)

$$ \frac{\sin i}{\sin r} = \text{constant} $$

This constant value is called the refractive index of the second medium with respect to the first.

Refractive Index

Light propagates with different speeds in different media. Light travels fastest in vacuum with speed of 3 × 108 m s-1. In air, the speed of light is only marginally less, compared to that in vacuum. It reduces considerably in glass or water. The value of the refractive index for a given pair of media depends upon the speed of light in the two media.

If c is the speed of light in air and v is the speed of light in the medium, then, the refractive index of the medium n is given by

$$ n = \frac{c}{v} $$

Refraction by Spherical Lenses

A transparent material bound by two surfaces, of which one or both surfaces are spherical, forms a lens.

A lens may have two spherical surfaces, bulging outwards. Such a lens is called a convex lens. It is thicker at the middle as compared to the edges. Convex lens converges light rays. Hence convex lenses are also called converging lenses.

Concave lens is bounded by two spherical surfaces, curved inwards. It is thicker at the edges than at the middle. Such lenses diverge light rays. Such lenses are also called diverging lenses.

Image Formation by Lenses

  1. A ray of light from the object, parallel to the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens. In case of a concave lens, the ray appears to diverge from the principal focus located on the same side of the lens.
  2. A ray of light passing through a principal focus, after refraction from a convex lens, will emerge parallel to the principal axis. A ray of light appearing to meet at the principal focus of a concave lens, after refraction, will emerge parallel to the principal axis.
  3. A ray of light passing through the optical centre of a lens will emerge without any deviation.

Lens Formula and Magnification

This formula gives the relationship between object-distance (u), image-distance (v) and the focal length (f).

$$ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} $$

Magnification

The magnification produced by a lens is defined as the ratio of the height of the image and the height of the object.

$$ m = \frac{h'}{h} = \frac{v}{u} $$

Power of a Lens

The ability of a lens to converge or diverge light rays depends on its focal length. For example, a convex lens of short focal length bends the light rays through large angles, by focussing them closer to the optical centre. Similarly, concave lens of very short focal length causes higher divergence than the one with longer focal length. The degree of convergence or divergence of light rays achieved by a lens is expressed in terms of its power.

The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P.

$$ P = \frac{1}{f} $$

The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D. If f is expressed in metres, then, power is expressed in dioptres.

The power of a convex lens is positive and that of a concave lens is negative.