Light: Reflection and Refraction

REFLCTION OF LIGHT

There are two laws of reflection of light

The angle of incident is equal to the angle of reflection, and
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.

SPHERICAL MIRRORS

A spherical mirror, whose reflecting surface is curved inwards that is called concave mirror. A spherical mirror, whose reflecting surface is curved outwards, is called a convex mirror. The centre of the reflecting surface of a spherical mirror is a point called the pole (P). It lies on the surface of the mirror. The reflecting surface of a spherical mirror forms a part of a sphere. The center point of this sphere is called the center of curvature of the spherical mirror (C). It lies in front of it, and lies behind the mirror in case of a convex mirror. The radius of the sphere is called the radius of curvature of the mirror (R). The straight line passing through the pole (P) and the centre of curvature(C) of a spherical mirror is called the principal axis.

Image Formation by Spherical Mirrors

1. A ray parallel to 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, on the concave or convex mirror is reflected obliquely. The incident and reflected rays at the point of incidence make equal angles with the principal axis.

REFRACTION OF LIGHT

Light does not travel in the same direction in all media. Whenever light travels obliquely from one medium to another, its direction of propagation changes. This phenomenon is known as refraction of light.

There are two laws of refraction of light

The incident ray , the refracted ray and the normal to the surface of separation of two transparent media at the point of incident, all lie in the same plane.
The ratio of sign of angle of incident to the sine of angle of refraction is a constant, for the light of a given color and for the given pair of media.

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

sin i/ sin r = constant

The Refractive Index

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

The light propagates with different speeds in different media. Light travels the fastest in vacuum with the highest speed of 3×10⁸ ms^-1.

A ray of light traveling from medium 1 with speed v₁ into medium 2 with speed v₂ .The refractive index of medium 2 with respect to medium 1 is represented by n_21.

n₂₁ = (speed of light in medium 1/ speed of light in medium 2) = v₁/v₂

The refractive index of medium 1 with respect to medium 2, represented as n₁₂

n₁₂ =(speed of light in medium ₂/ speed of light in medium₁) = v₂/v₁

If medium 1 is vacuum or air, then the refractive index of medium 2 is called the absolute refractive index (refractive index) of the medium represented as n₂.

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

n_m=(speed of light in air / speed of light in the medium) = c/v

The refractive index of water, n_w = 1.33

The refractive index of crown glass, n_g = 1.52

Refraction by Spherical Lenses

Double convex lens or convex lens has two spherical surfaces, bulging outwards. Double concave lens is bounded by two spherical surfaces, curved inwards.

Each spherical surfaces of a lens forms a part of a sphere. The centers of these surfaces are called centers of curvature of the lens. The straight line passing through the two centers of curvature (C1and C2) of a lens is called its principal axis. The central point O of a lens is its optical centre. The light through the optical centre of a lens passes without suffering any deviation.

The rays of light parallel to the principal axis, after refraction from the lens are converging to a point on the principal axis known as principal focus of the lens.

Image Formation by Lenses

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 concave lens, the ray appears to diverge from the principal focus located on the same side of the lens.
A ray of light passing though 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.
A ray of light passing through the optical centre of a lens will emerge without any deviation.

Power of a Lens

A convex lens of short focal length bends the light rays through large angles and focal them closer to the optical centre. Concave lens of very short focal length causes higher divergence than a lens of longer focal length. The power (P) of a lens is defined as the reciprocal of its focal length (f).

Power P = 1/f

The SI unit of power of a lens is dioptre (D). 1 dioptre is the power of a lens whose focal length is 1 metre.1D=1m^-1. The power of a convex lens is positive and that of a concave lens is negative.

Summary of the Chapter

Light is that energy through which we can see objects.
Light seems to travel in straight lines.
Mirrors and lenses form images of objects. Images can be either real or virtual.
The reflection surfaces obey the laws of reflection. The refracting surfaces obey the laws of refraction.
New Cartesian Sign Conversions are followed for spherical mirrors and lenses.
Mirror formula. 1/v + 1/u = 1/f, gives the relationship between the objects distance (u), image distance (v), and focal length (f) of a spherical mirror.
The focal length of a spherical mirror is equal to half its radius of curvature

(f = R/2).

The magnification produced by a mirror or lenses is the ratio of the height of the image to the height of the object.
A concave mirror may form real or virtual image depending on position of object. A convex mirror forms only virtual, erect and diminished image.
A light ray traveling obliquely forms a denser medium to rarer medium bends away from the normal. A light ray bends towards the normal when it travels obliquely from a rarer to a denser medium.
Light travels in vacuum with a constant speed of 3×10⁸ m s^-1. The speed of light is different in different media.
The refractive index of a transparent medium is the ratio of the speed of light in vacuum to that in the medium.
In case of a rectangular glass slab, the refraction takes place at both air-glass interface and glass-air interface. The emergent ray is parallel to the direction of incident ray.
Lens formula:1/v – 1/u = 1/f,gives the relationship between the object-distance(u),