Diffraction of Light by Single slit

\(b\ \sin\ \theta=n\ \lambda\ (dark\ fring)\)

Linear width of central maxima

Width of central maxima \(=\ \frac{2\ \lambda}{b}\)

Angular width \(=\ \frac{2\ D\ \lambda}{b}\)

\(b\ \sin\ \theta=\ (2n\ +\ 1)=\frac{\lambda}{2}\)

(for maxima bright fringe)

Young's Double Slit Experiment

→  Path difference

  \(\bullet\)   For bright fringe

        \(\Delta\ \phi=n\ \lambda\)

\(\bullet\)   For dark fringe

     \(\Delta\ \phi=\ (n\ +\ \frac{1}{2})\ \lambda\)

Based in interference of light distance between nth dark fringe and central fringe.

            \(x_n\ = \ \frac{(2\ n\ +\ 1)\ \lambda\ D}{2\ \lambda}\)

d = distance between slits.

Interference of light

Two waves superimpose to form a resultant wave of greater or lower or same amplitude

                \(I= (\sqrt {I_1}\ +\ \sqrt {I_2})^2\\ \beta \ =\ (A_1\ +\ A_2)^2\)

►  For constructive Interference

               \(A=A_1\ +\ A_2\)

►  For destructive Interference 

             \(A=(A_1\ \sim A_2)\)

Coherent Source

Two sources of light are said to be coherent if the initial phase difference between the waves entitled by the sources remains constant with time, otherwise they are called incoherent source of light.

 Wave Optics Describes the connection between waves and rays of light. According to wave theory of light, light is a form of energy which travels through a medium in the form of transverse wave.
Wave front The locus of all those particles which are vibrating in the same phase at any instant is called wave front. Thus, wave front is a surface having same phase of vibrating particles at any instant at every point on it.
 Phase Speed Phase speed is the speed with which wave front moves and it is equal to wave speed.
 The shape of wavefront due to a
(i) point source is spherical
(ii) line source is cylindrical
(iii) source at infinity is a plane.
 A line perpendicular to a wave front is called a ray. The direction of rays are always perpendicular to the wave front along the direction of propagation of wave.

Huygens’ Principle

 Huygens’ principle is essentially a geometrical construction, which gives the shape of the wave front at any time, allows us to determine the shape of the wave front at a later time. According to Huygens’ principle,
(i) Every point on a wave front behaves like a light source and emits secondary wavelets.
(ii) The secondary wavelets spread in all directions in space (vacuum) with the velocity of light.
(iii) The envelope of wave front of secondary wavelets, after a given time, along forward direction gives the new position of wave front.
The laws of reflection and refraction can be verified using Huygens’ wave theory.
Huygens’ wave theory successfully explains the phenomenon of interference, diffraction and polarisation.
As, frequency v is characteristic of the source, therefore v = 1/T remains the same as light travels from one medium to another.
 Wavelength is inversely proportional to refractive index (μ) of the medium
i.e. λ’ = λ/μ