Light reflection and refraction

REFLECTION OF LIGHT:

Laws of reflection:

(I) The angle of incidence is equal to the angle of reflection.

(II)The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane.

The laws are applicable for all types of reflecting surfaces including spherical surfaces. As we are familiar with formation of images by plane mirrors, they always form virtual and erect images.

Spherical mirrors:

The mirrors, whose reflecting surfaces are spherical, are called spherical mirrors. A spherical mirror, whose reflecting surface is curved inwards is called a concave mirror. A spherical mirror, whose reflecting surface is curved outwards is called a convex mirror.

The Centre of the reflecting surface of the spherical mirror is a point called Pole. It is represented by the letter ‘P.’ 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. It is reflected by letter ’C’. Centre of curvature is not a part of the mirror. It lies outside its reflecting surface.
The radius of the sphere, which is formed by the reflecting surface of the spherical mirror, is called radius of curvature. It is represented by the letter ‘R’. The line passing through the pole and Centre of curvature is called the principal axis. Principle axis is normal to the mirror and its pole.
When we pass light rays through the spherical mirror, reflected rays appear to pass through a single point on the principal axis. This point is called the principle focus of mirror. It is represented by letter ‘F’.
The distance between the pole and the principle focus of a spherical mirror is called the focal length. It is represented by the letter ‘f’. The diameter of the reflecting surface of the spherical mirror is called Aperture.
The focal length said to be half the radius of curvature (R=2f). This implies that the principle focus of spherical mirror lies midway between the pole and the Centre of curvature.

Image formation by spherical mirror:

The nature, position and size of the image formed by a concave mirror depends on the position of the object with respect to the points Principal axis, focal point and Centre of curvature.

Following table shows the positions of image formed by concave.

Images formed by spherical mirrors using ray diagrams:

(I) If a ray travel parallel to the principal axis, after reflection, it will pass through the focus in case of concave mirror and diverge from the focus in case of convex mirror. As shown in figure 1.

(II) If a ray passes through the principal focus, after reflection it will pass parallel to the principal axis in both cases of concave and convex mirrors as shown in figure 2.

(III) The ray passing through the Centre of curvature of a concave mirror, after reflection, will be reflected back in the same path. This is because the incident ray fall on the mirror along the normal on the reflecting surface.

(IV) If a ray incident obliquely to the principal axis towards the pole of the concave mirror or convex mirror, it will reflect obliquely. Both the incident and reflected rays follows the laws of reflection at the point of incidence.

Uses of the concave mirror:

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

Images formed by convex mirror:

Figure (a) represents the image formed by the convex mirror when object is at infinity and figure (b) represents the image formed by the convex mirror when object is at finite distance. The results of the images formed by the convex mirror are shown in the below table.

Nature, position and relative size of the image formed by a convex mirror.

Uses of convex mirror:

Convex mirrors are commonly used as rear-view mirrors in vehicles.

Sign conversion for Reflection by spherical mirrors:

While dealing with the reflection of light by spherical mirrors, we have to follow a set of sign conversions called the New Cartesian Sign Conversion.

In this conversion, pole of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis of the coordinate system.

The conversations are as follows:

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.
All distances parallel to the principal axis are measured from the pole of the mirror.
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.

Distances measured perpendicular to and above the principal axis(along + y-axis) is taken as positive.
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 is called image distance(v).

We have a relation between these two and focal length(f) given by the mirror formula.

1/v + 1/u = 1/f

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

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. It is represented by letter ‘m’.

m= (height of the image)/ (height of the object)

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

Magnification(m)=v/u

The negative sign in the value of the magnification indicates that the image is real and positive sign indicates that the image is virtual.

REFRACTION OF LIGHT:

Light does not travel in same direction in all mediums. The direction of light changes when it passes through different mediums. This phenomenon is known as Refraction of light.

Laws of refraction of light:

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 sine of angle of incidence to the sine angle of refraction is a constant, for the light of a given color and given part of the media. This law is also is known as Snell’s law of refraction. (This is true for angle 0<I <90⁰)

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

(Sin i)/(sin r) = constant

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

The Refractive index:

The refractive index can be linked to an important quantity, the relative speed of the propagation of light in different mediums. It turns out that light propagates with different speeds in different mediums.

Light travels fastest in vacuum with speed of 3×10⁸m s^-1. In air, the speed of light is marginally less, compared to in vacuum. It reduces considerably in glass and water.

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

n_m= speed of light in air / speed of light in medium =c/v

The absolute refractive index of the medium is simply called its refractive index.

The following table shows the refractive index of several media.