**Interference
of Light**

When two waves of exactly same frequency travels in a medium, in the same direction simultaneously then due to their superposition, at some points intensity of light is maximum while at some other point’s intensity is minimum. This phenomenon is called Interference of light. It is of following two types

(1) **Constructive
interference: **When the waves meet a point with same phase, constructive
interference is obtained at that point i.e. maximum light

(i)Phase difference between the waves at the point of observation \(\phi ={{0}^{0}}\,\,\left( or \right)\,\,2n\pi \)

(ii) Path difference between the waves at the point of observation \(\Delta =n\lambda \) i.e. even multiple of \(\lambda /2\)

(iii) Resultant amplitude at the point of observation will be maximum, \({{A}_{\max }}={{a}_{1}}+{{a}_{2}}\) if \({{a}_{1}}={{a}_{2}}={{a}_{0}}\Rightarrow {{A}_{\max }}=2{{a}_{0}}\)

(iv) Resultant intensity at the point of observation will be maximum,\({{I}_{\max }}={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\) \(={{\left( \sqrt{{{I}_{1}}}+\sqrt{{{I}_{2}}} \right)}^{2}}\) if \({{I}_{1}}={{I}_{2}}={{I}_{0}}\Rightarrow {{I}_{\max }}=4{{I}_{0}}\)

(2)**
Destructive interference: **When the wave meets a point with opposite phase,
destructive interference is obtained at that point i.e. minimum light

(i) Phase difference, \(\phi ={{180}^{0}}\,\,\,(or)\,\,\,\left( 2n-1 \right)\pi \,\,;\,\,n=1,2,3,4….\) (or) \(\left( 2n+1 \right)\pi \,\,;\,n=0,1,2,3……\)

(ii) Path difference, \(\Delta =\left( 2n-1 \right)\frac{\lambda }{2}\) i.e. odd multiple of \(\lambda /2\)

(iii) Resultant amplitude at the point of observation will be minimum, \({{A}_{\min }}={{a}_{1}}-{{a}_{2}}\) if \({{a}_{1}}={{a}_{2}}\Rightarrow {{A}_{\min }}=0\)

(iv) Resultant intensity at the point of observation will be minimum, \({{I}_{\min }}={{I}_{1}}+{{I}_{2}}-2\sqrt{{{I}_{1}}{{I}_{2}}}={{\left( \sqrt{{{I}_{1}}}-\sqrt{{{I}_{2}}} \right)}^{2}}\)If \({{I}_{1}}={{I}_{2}}={{I}_{0}}\Rightarrow {{I}_{\min }}=0\)

(3) **Super
position of waves of random phase difference: **When two or more waves having
random phase difference between them super impose, then no interference pattern
is produced. Then the resultant intensity is just the sum of the two
intensities.