JEE Main & Advanced Physics Wave Optics / तरंग प्रकाशिकी Coherence

The phase relationship between two light waves can very from time to time and from point to point in space. The property of definite phase relationship is called coherence.

(1) Temporal coherence : In a light source a light wave (photon) is produced when an excited atom goes to the ground state and emits light.

(i) The duration of this transition is about \[{{10}^{-9}}\] to \[{{10}^{-10}}\] sec.  Thus the emitted wave remains sinusoidal for this much time. This time is known as coherence time \[({{\tau }_{c}})\].

(ii) Definite phase relationship is maintained for a length \[L=c{{\tau }_{c}}\] called coherence length.  For neon \[\lambda =6328\,\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,\,{{\tau }_{c}}\approx {{10}^{-10}}\] sec and L = 0.03 m.

For cadmium \[\lambda =6438\,\,\overset{\text{o}}{\mathop{\text{A}}}\,,\,\,{{\tau }_{c}}={{10}^{-9}}\] sec and L = 0.3 m

For Laser \[{{\tau }_{c}}={{10}^{-5}}\] sec and L = 3 km  

(iii) The spectral lines width \[\Delta \lambda \] is related to coherence length L and coherence time \[{{\tau }_{c}}\]. \[\Delta \lambda \approx \frac{{{\lambda }^{2}}}{c{{\tau }_{c}}}\] or \[\Delta \lambda \approx \frac{{{\lambda }^{2}}}{L}\]

(2) Spatial coherence : Two points in space are said to be spatially coherence if the waves reaching there maintains a constant phase difference

Points P and Q are at the same distance from S, they will always be having the same phase. Points P and \[P'\] will be spatially  coherent if the distance between P and \[P'\] is much less than the coherence length i.e. \[PP'<<c{{\tau }_{c}}\]

(3) Methods of obtaining coherent sources : Two coherent sources are produced from a single source of light by two methods (i) By division of wavefront and (ii) By division of amplitude

(i) Division of wave front : The wave front emitted by a narrow source is divided in two parts by reflection, refraction or diffraction.

The coherent sources so obtained are imaginary. There produced in Fresnel's biprism, Llyod's mirror Youngs' double slit etc.

(ii) Division of amplitude : In this arrangement light wave is partly reflected (50%) and partly transmitted (50%) to produced two light rays.

The amplitude of wave emitted by an extend source of light is divided in two parts by partial reflection and partial refraction.

The coherent sources obtained are real and are obtained in Newton's rings, Michelson's interferrometer, colours in thin films.