IEMDaily - Video Lecture Notes

Definition

Different kinds of waveforms

The wavefronts of a wave originating from a point source are spherical.
The wavefronts of a wave going along a fixed direction are planes perpendicular to that direction.

Example

Shape of emergent wavefront when plane wavefront is incident on an optical instrument

For a point source of light, the shape of wavefront can be considered to be plane at very large distance from the source. If a point source of light is placed at the focus of a thin spherical lens, then the shape of the wavefront for emerged light may be plane. The shape of the wavefront for the light incident on a thin spherical lens (kept in vacuum) is plane, the shape of the wavefront corresponding to emergent light would be always spherical. And according to convention, direction of wave propagation is along the normal to wavefront.The wavefront of a point source of light is spherical. A sphere with large radius is like a plane at its surface. Thus for a point source of light, the shape of wavefront can be considered to be plane at very large distance from the source. Beam of light from a point source emerges parallel to principle axis when kept at focus of a thin spherical lens. Thus the wavefront emergent from the lens is planar.

Definition

Reflection using Huygen's principle

A plane wave AB is incident at an angle

i

on a reflecting surface MN. If

v

represents the speed of the wave in the medium and if

τ

represents the time taken by the wavefront to advance from the point B to C then the distance
BC =

v τ

In order the construct the reflected wavefront we draw a sphere of radius

v τ

from the point A. Let CE represent the tangent plane drawn from the point C to this sphere. Obviously
AE = BC =

v τ

If we now consider the triangles EAC and BAC we will find that they are congruent and therefore, the angles

i

and

r

would be equal. This is the law of reflection.

Definition

Refraction using Huygen's principle

Let PP' represent the surface separating medium 1 and medium 2, and

v_{1}

and

v_{2}

represent the speed of light in the mediums. We assume a plane wavefront AB propagating in the direction A'A incident on the interface at an angle i. Let

τ

be the time taken by the wavefront to travel the distance BC. Thus,

B C = v_{1} τ

In order to determine the shape of the refracted wavefront, we draw a sphere of radius

v_{2} τ

from the point A in the second medium. Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE =

v_{2} τ

and CE would represent the refracted wavefront. If we now consider the triangles ABC and AEC, we readily obtain

\sin i = \frac{B C}{A C} = \frac{v_{1} τ}{A C}

\sin r = \frac{A E}{A C} = \frac{v_{2} τ}{A C}

where

i

and

r

are the angles of incidence and refraction, respectively.
Substituting the values of

v_{1}

and

v_{2}

in terms of

n_{1}

and

n_{2}

we get the Snell's Law:

n_{1} \sin i = n_{2} \sin r

Definition

Describe the drawbacks of Huygen's Wave Theory

The limitations of Huygens Wave Theory of Light are as follows:

It could not explain rectilinear propagation of light
It could not explain phenomenon of polarisation of light and phenomenon like Compton Effect, photoelectric effect.
Michelson and Morley experiment concluded that there is no ether drag when earth moves through it. This proves ether doesnt exist. All the other attempts to detect luminiferous ether failed, which proves that luminiferous ether does not exist.

Definition

Effect on wavelength of light in medium change

When a light ray goes from one medium to another its frequency remain invariable.
Since:
velocity: