Light Reflection and Refraction

Chapter:- 4

Light

Light Reflection and Refraction

Light is a form of energy that enables us to see. An object reflects the light rays that fall on it. Speed of light in vacuum or in air is 3 x 108 m/s.

Light beam can be of three types

Convergent Beam It is a beam of light in which the width of beam goes on decreasing as the rays proceed forward and ultimately all the rays meet at a point.

Divergent Beam It is a beam of light in which the width of the beam goes on increasing as the rays proceed forward. Here, the rays spread out from a point.

Parallel Beam It is a beam of light in which the rays move parallel to one another. The width of the beam remains constant as the rays proceed forward.

Reflection of Light

The phenomenon of bouncing back of light rays in the same medium on striking a smooth surface is called reflection of light.

Laws of Reflection

There are two laws of reflection

• Angle of incidence is always equal to the angle of reflection.

• The incident ray, the reflected ray and the normal at the point of incidence, all lie in the same plane.

Image

If light rays coming from a point after reflection meet at another point or appear to meet at another point, then the second point is called the image of the first point.

Image is of two types

• Real Image If the light rays coming from a point actually, meet after reflection, and then the image formed is called a real image.
• Virtual Image If the light rays coming from a point, after reflection does not meet actually, but appear to meet at another point, then the image formed is called a virtual image.

Comparison between Real and Virtual Images

Mirrors

Mirrors

Mirror is a polished surface like glass, which reflects almost all the light that is incident on it.

Mirrors are of two types

Plane Mirror

If the reflecting surface of a mirror is plane, then the mirror is called a plane mirror.

Reflection from a plane mirror is shown Object in the figure given alongside.

Image Formed By a Plane Mirror Has Following Properties

• It is always virtual and erect.
• The size of image is equal to the size of the object.
• The image formed is as far behind the mirror al the object is in front of it.
• The image is laterally inverted. (i.e. left seems to be right and vice-versa)

Uses of Plane Mirrors

• Plane mirrors are commonly used as looking glass because the reflection that forms the image is always erect and laterally inverted but they are always virtual.
• Used in making periscopes which is used in submarines?
• Used as blind turns of some busy roads, to see the vehicles coming from other side.
• They are used to make kaleidoscope, a toy which produces beautiful patterns from colored paper, pieces of glass or small colored beads.

Spherical Mirror

If the reflecting surface of the mirror is spherical, then the mirror is called a spherical mirror.

Spherical mirrors are of two types

(i):- Concave Mirror or  Convergent Mirror

(ii):- Convex Mirror or Divergent Mirror

Concave Mirror or Convergent Mirror

The spherical mirror with inward curved reflecting surface is called concave mirror. A beam of light generally converges after reflection from its surface, hence it is also caller convergent mirror.

Convex Mirror or Divergent Mirror

The spherical mirror with outward curved reflecting surface is called convex mirror. A beam of light generally diverges after reflection from its surface, hence it is also called divergent mirror.

Centre of Curvature

Centre of curvature of a spherical mirror is the centre of the imaginary sphere of which, mirror is a part. In case of concave mirror, the centre of curvature lies in front of it while in case of convex mirror, the centre of curvature lies behind it.

Radius of curvature of a spherical mirror is the radius of Imaginary sphere of which, mirror is a part: In the figure, it is shown by R.

Pole

Pole of the spherical mirror is the mid-point of its reflecting surface. In the figure, it is shown by P.

Principal Axis

The principal axis of a spherical mirror is the line joining the pole and centre of curvature.

Aperture

The diameter of the reflecting surface of spherical mirror is; ailed its aperture. It is equal to the straight line distance between two ends of the mirror.

Principal Focus of a Spherical Mirror

It is a point on the principal axis of the mirror at which the light rays coming parallel to principal axis after reflection actually meet or appear to be coming from. It is represented by F.

Focal Length

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

Representation of images formed by spherical Mirrors, Using Ray Diagrams

Representation of images formed by spherical Mirrors, Using Ray Diagrams

The reflection follows the same two rules everywhere. The intersection of at least two reflected rays gives the position of image of the point object.

The following rays can be considered for locating the image

• The rays coming parallel to the principal axis passes through the focus after reflection or appears to come from focus.

• The rays coming through the focus of mirror or coming towards focus, becomes parallel to principal axis.

• The light ray coming through centre of curvature or towards centre of curvature reflects on the same path.

• A ray incident obliquely to principal axis, towards a pole P of the concave or convex mirror is reflected obliquely, following the laws of reflection. i.e. i=∠r

Images Formation by a Concave Mirror

Given Below illustrates the ray diagram along with the position and nature of image, formed by a concave mirror for various positions of the object.

Formation of Image by Concave Mirror for Different Positions of Object

(1):- When Position of Object → at Infinity Position of Image → at focus or in the focal plane Nature and size of Image → Real, Inverted, extremely diminished in size.

(2):- When Position of Object → Beyond the centre of curvature but at finite distance

Position of Image → between focus and the centre of curvature

Nature and size of Image → Real, inverted, diminished.

(3):- Position of Object → At the centre of curvature

Position of Image → at the centre of curvature

Nature and size of Image → Real, inverted, and equal to the object.

(4):- Position of Object → Between focus and centre of curvature

Position of Image → beyond the centre of curvature

Nature and size of Image → Real, inverted, and bigger than object.

(5):- Position of Object → at the focus

Position of Image → at infinity

Nature and size of Image → Real, inverted, and extremely magnified.

(6):- Position of Object → between the pole and focus

Position of Image → behind the mirror

Nature and size of Image → Virtual erect and magnified

Uses of Mirrors

Uses of Concave Mirrors

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

Formation of Image by Convex Mirror for Different Positions of Object

(1):- When Position of Object → at Infinity

Position of Image → at the principal focus

Nature and size of Image → Virtual erect and extremely diminished

(2):- When Position of Object → between infinity and the pole (i.e., at finite distance)

Position of Image → between the principal focus and the pole

Nature and size of Image → Virtual erect and diminished

Uses of Convex Mirrors

Convex mirrors are commonly used as rear view mirrors in vehicles because they always give an erect image and have wider field of view as they are curved outwards.

Big convex mirrors are used as shop security mirrors; the shop owner can keep an eye on the customers to look for thieves and shoplifters among them.

Sign Convention for Reflection by Spherical Mirrors

While dealing with the reflection of light by spherical mirrors, we shall follow a set of sign convention called the new Cartesian sign convention based on Cartesian coordinates.

The conventions are as follows

• The object is always placed to the left of the mirror.
• All distances parallel to principal axis (x – axis) are measured from the pole of the mirror.
• Distances to the left of pole (– ve x – axis) are negative. Distances to the right of pole (+ ve x – axis) are positive.

• Distances measured perpendicularly above the principal axis (along + y – axis) are taken as positive.
• Distances measured perpendicularly below the principal axis (along – y – axis) are taken as negative.

Mirror Formula

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

The distance of the principal focus from the pole is called focal length (f). The relation between quantities (u, v and f) is called mirror formula.

This formula is valid in all situations for all spherical mirrors and for all positions of the object.

Linear Magnification

Linear 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 height of image to the height of object. It is represented by m.

Magnification is also related to the object distance (u) and image distance (v). It can be expressed as

Refraction of Light at Plane Surface

Refraction of Light

Change in path of light ray as it passes from one medium to another medium is called refraction.

When light travels from a rarer medium to a denser one; it bends towards the normal       (i > r) and when travels from a denser medium to a rarer one, it bends away from the normal

i = angle of incidence, r = angle of refraction.

Refraction of Light

Cause of Refraction

Speed of light is different in different media. It is lesser in denser medium and higher in rarer medium So when light entre a denser medium its speed reduces and it bends towards the normal and when it enters rarer medium, its speed increases and it bends away from the normal.

Everyday Examples of Refraction of Light

• The bottom of a tank or pond containing water appears to be raised due to refraction of light which takes place when light rays pass from the pool of water into the air.
• The letters appear to be raised when viewed through a glass slab placed over the document because of refraction of light.
• A pencil partially immersed in water appears to be broken because of the refraction of light coming from the part of pencil that is under water.
• A lemon kept in water in a glass tumbler appears to be bigger than its actual size, when viewed from the sides.

Refraction through a Rectangular Glass Slab

When a light ray enters in a glass slab then the emergent ray is parallel to the incident ray but it is shifted sideward slightly. In this case, refraction rakes place twice; first when ray enters glass slab from air and second when exits from glass slab to air. Where, i = angle of incidence, r = angle of refraction e = angle of emergence. Lateral Displacement The perpendicular distance between the emergent ray and incident ray when the light passes out of a glass slab is called lateral displacement.

Laws of Refraction

Refraction of light occurs according to the following laws

• 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.
• The ratio of sin of angle of incidence to the sin of angle of refraction for light of given color is constant for a given pair of media (Snell's law). It is expressed

This constant is known as refractive index (μ).

Refractive Index

The extent of the change in direction that takes place in a given pair of media is expressed in terms of the refractive index.

Refractive Index and Velocity

The value of 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 is

Lens

Lens

Lens is a transparent medium bounded by two surfaces of which, one or both surfaces are spherical.

Lenses are of two types

Convex or Converging Lens

A lens which is thicker at the centre and thinner at its end is called convex lens.

Note

• A convex lens is also known as converging lens because it converges a parallel beam of light rays passing through it.
• A double convex lens is simply called convex lens

Concave or Diverging Lens

A lens which is thinner at the centre and thicker at its end is called a concave lens.

Note

• A concave lens is also known as diverging lens because it diverges a parallel beam of light rays passing through it.
• A double concave lens is simply called concave lens.

Some Definitions Related to Lenses (Optical Center)

The centre point of a lens is known as its optical centre. Directed to which incident rays refract without any deviation in the path.

Centers of Curvature

The centers of the two imaginary spheres of which the lens is a part are called centers of curvature of the lens. A lens has two centers of curvature with respect to its two curved surfaces.

The radii of the two imaginary spheres of which the lens is a part are called radii of curvature of the lens. A lens has two radii of curvature. These may or may not be equal.

Principal Axis

The imaginary line joining the two centers of curvature is called principal axis of lens. Principal axis also passes through the optical centre.

Principal Focus

Lens has two principal foci

(a) First Principal Focus It is a point on the principal axis of lens, the rays starting from or directed to which, become parallel to principal axis after refraction.

(b) Second Principal Focus It is the point on the principal axis at which the rays coming parallel to the principal axis, converge on the other side of lens (convex) or appear to meet on the same side of lens (concave), after refraction from the lens.

Focal Length of Lens

The distance between focus and optical centre of lens is called focal length of lens.

Aperture

The effective diameter of the circular outline of a spherical lens is called its aperture.

Image Formation in Lenses Using Ray Diagrams

We can represent image formation by lenses using ray diagrams.

For drawing ray diagrams in lenses alike spherical mirrors, we consider any two of the following rays

• Rays which are parallel to the principal axis after refraction will pass through principal focus in case of convex lens and will appear to be coming from principle focus in case of concave lens

• Ray passing through or directed to the focus will emerge parallel to the principal axis.

• Ray directed to optical centre will emerge our undedicated.

Formation of Image by a Concave Lens

There are two positions of object. Firstly, when the object is at infinity

Formation of Image by concave lens for Second Position of object

The second position is when the object is at finite distance from the lens.

Sign Convention for Spherical Lenses

Sign convention for lenses is same as that for mirrors. The focal length of a convex lens is positive and that of a concave lens is negative.

Lens Formula

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

Linear Magnification

The ratio of height of image to the height of object is called linear magnification (m).

Linear magnification is positive, when image formed is virtual and linear magnification is negative, when image formed is real.

Power of a Lens

The ability of a lens to converge or diverge light rays is called power (P) of the lens. It is defined as the reciprocal of focal length i.e. P =1/f (in metre).

Its SI unit is dioptre (D) (1D =1 m-1).

If f is expressed in metres then, power is expressed in dioptres. Thus, dioptre is the power of a lens whose focal length is 1 metre. If focal length is given in centimetre, then

For concave lens, power and focal length are – ve.

For convex lens, power and focal length are + ve.

Power of Combination of Lenses

When two or more thin lenses are used in combination, the equivalent focal length (f) and power of the combination (P) can be calculated as

And P = P1 + P2 +…

Magnification of lens in combination (m) is given by

Note

• The use of combination of lenses increases the sharpness of image; also the image produced is also free from many defects.
• The additive property of the powers of the lenses can be used to design lens systems to minimize certain defects in images produced by a single lens. Such a lens system, consisting of several lenses, in contact, is commonly used in designing of camera lenses and the objectives of microscopes and telescopes.