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Light - Reflection and Refraction

Chapter: Light – Reflection and Refraction

Light is a form of energy which gives us the sensation of sight or vision. Light is not visible to us. It shows the phenomena of reflection, refraction and dispersion. Light is also defined as an electromagnetic wave which does not require a material medium for propagation.

Reflection of Light

Laws of reflection of light:

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

These laws of reflection are applicable to all types of reflecting surfaces including spherical surfaces.

Spherical Mirrors

A spherical mirror is the mirror whose reflecting surface is as a part of a hollow sphere.

A plane mirror will produce image of the same size. 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. A concave mirror will produce a magnified image whereas a convex mirror will produce a diminished image.

Terms involved in spherical mirrors

1. Center of curvature

Center of curvature is the center of the sphere of glass of which the mirror is a part.

2. Radius of curvature

Radius of curvature is the radius of sphere of glass of which mirror is a part.

3. Pole

Middle part of the mirror is called pole

4. Principal axis

Principal axis of a spherical mirror is the straight line joining the centre of curvature and pole of the mirror.

5. Focus

The midpoint of the line drawn from center of curvature and pole is called focus

Representation of Images Formed by Spherical Mirrors Using Ray Diagrams

The various rules for obtaining images formed by a concave mirror.

Rule 1.

 

 

When an incident ray of light is parallel to the principal axis of a concave mirror, its reflected ray must pass through the principal focus of the concave mirror.

 

Rule 2.

 

 

When an incident ray of light passes through the focus of a concave mirror, its reflected ray is parallel to the principal axis.

 

Rule 3.

 

 

If an incident ray of light passes through the center of curvature of a concave mirror, it is reflected back along the same path.

 

Rule 4.

 

 

A ray incident obliquely to the principal axis, towards point P on the concave or a convex mirror is reflected obliquely. The incident and reflected rays make equal angles with the principal axis.

 

Uses of concave mirrors

Concave mirrors are generally used in search-lights, torches and vehicles headlights to get powerful parallel beams of light. Also they are 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 mirrors in vehicles. These mirrors are fitted on the sides of the vehicle, enabling the driver to see traffic behind them to ensure safe driving. Convex mirrors are mostly 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.

Mirror Formula and Magnification

The relation between the object distance (u), image distance (v) and focal length (f) is given by mirror formula which is expressed as

 

 

Let us define the above three terms as below:

 

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).

Magnification

It is expressed as the ratio of the height of the image to the height of the object. It is usually represented by the letter m.

 

Image formation by a concave mirror for different positions of the object

 

 

Image formation by a convex mirror for different positions of the object

 

 

Refraction of Light

 

Refraction is defined as the bending of light when it passes from one medium to another. The refraction of light takes place when it travels from one medium to another because the speed of light is different in the two medium.

Laws of refraction

There are two laws of refraction

  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 color and for the given pair of media. This law is also known as Snell’s law of refraction.

The Refractive Index

If i is the angle of incidence and r is the angle of refraction, then

 

 

This constant value is called the refractive index. It has no units as it is a ratio of two similar quantities. The value of the refractive index for a given pair of media depends upon the speed of light in the two media.

 

Refraction by Spherical Lenses

There are two types of lenses.

1. Convex lens

A lens may have two spherical surfaces, bulging outwards. Such a lens is called convex lens. It is thicker at the center than at the edges and has a real focus. It converges a parallel beam of light on refraction through it.

2. Concave lens

A concave lens is bounded by two spherical surfaces, curved inwards. It is thinner at the center than at the edges and has a virtual focus. It diverges a parallel beam of light on refraction through it.

Image Formation in Lenses Using Ray Diagrams

The rules followed by light rays while passing

Rule 1.

An incident ray parallel to the principal axis of a lens, passes (in case of convex lens) or appears to be coming from the focus( in case of concave lens) after refraction.

 

 

Rule 2.

 

An incident ray passing through the optical center of a lens (concave or convex) goes straight after refraction.

 

 

Rule 3.

 

An incident ray passing through the focus of a convex lens becomes parallel to the principal axes after refraction.

 

 

Lens Formula and Magnification

 

The lens formula gives the relationship between object distance (u), image-distance (v) and the focal length (f ). The lens formula is expressed as

 

 

Magnification

 

The magnification produced by a lens, similar to that for spherical mirrors, is defined as the ratio of the height of the image and the height of the object. It is represented by the letter m. If h is the height of the object and h′ is the height of the image given by a lens, then the magnification produced by the lens is given by,

 

Nature, position and relative size of the image formed by a convex lens for various positions of the object

 

 

 

Nature, position and relative size of the image formed by a concave lens for various positions of the object

 

 

Power of a Lens

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

P = 1/f

The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D.If f is expressed in meters, then, power is expressed in dioptres. Thus,1 dioptre is the power of a lens whose focal length is 1 meter.

1D = 1m-1.  The power of a convex lens is positive and that of a concave lens is negative.

Opticians prescribe corrective lenses indicating their powers.