(i) The phenomenon of addition or superposition of two light waves which produces increase in intensity at some points and decrease in intensity at some other points is called interference of light. (ii) Consider two light waves from the two sources `S_1` and `S_2` meeting at a point P. The wave from `S_1` at an instant t at P is,
` y_1 =a_1 sin omega t`
The wave form `S_2` at an instant t at P is,
`y_2 = a_2 sin (omega t + phi)`
(iii) The two waves have different amplitudes `a_1` and `a_2` same angular frequency `omega`, and a phase difference of `phi` between them. The resultant displacement will be given by,
` y = y_1 + y_2 = a_1 sin omega t = a_1 sin_2 (omega t + phi)`
(iv) The simplification of the above equation by using trigonometric identities,
` y = A sin (omega t + theta)`
Where , `A = sqrt(a_1^2 + a_2^2 + 2 a_1 a_2 cos phi) " " ....(1)`
` theta = tan^(-1) (a_2 sin phi)/(a_1 + a_2 cos phi)`
The resultant amplitude is maximum,
` A_(max) = sqrt((a_1 + a_2)^2) , " when " phi = 0, pm 2pi , pm 4pi .....`
The resultant amplitude is minimum,
` A_("min") = sqrt((a_1 + a_2)^2) , " when " phi = pm pi , pm 3pi , pm 5 pi.....,`
The intensity of light is proportional to square of amplitude,
` I prop A^2`
Now, equation (1) becomes,
` I prop I_1 + I_2 + 2 sqrt(I_1I_2) cos phi " " ....(2)`
(v) In equation (2) if the phase difference, `phi = 0, pm 2pi, pm 4pi .....,` it corresponds to the condition for maximum intensity of light called as constructive interference. The resultant maximum intensity is,
` I_(max) prop (a_1 +a_2)^2 prop I_1 + I_2 + 2 sqrt(I_1 I_2)`
(vi) In equation (2) if the phase difference, `phi = pm pi, pm 3pi, pm 5pi .....,` it corresponds to the condition for minimum intensity of light called destructive interference. The resultant minimum intensity is,
` I_("min") prop (a_1 - a_2)^2 prop I_1 + I_2 - 2 sqrt(I_1 I_2)`
