Two light waves coming from S 1 and S 2 at the point P on the screen is E 1 = E 0 sin ω t and E 2 = E 0 sin ( ω t + φ ) . The intensity at point P will be proportional to

Question

Two light waves coming from S 1 ​ and S 2 ​ at the point P on the screen is E 1 ​ = E 0 ​ sin ω t and E 2 ​ = E 0 ​ sin ( ω t + φ ) . The intensity at point P will be proportional to

TestHub · Accepted Answer

The resultant electric field at point P is given by the principle of superposition:

$E = E_{1} + E_{2}$

$E = E_{0} sin ω t + E_{0} sin (ω t + φ)$

Using the trigonometric identity $sin A + sin B = 2 sin (\frac{A + B}{2}) cos (\frac{A - B}{2})$ :

$E = 2 E_{0} cos (\frac{φ}{2}) sin (ω t + \frac{φ}{2})$

The amplitude of the resultant wave is $A = 2 E_{0} cos (\frac{φ}{2})$ .

Since the intensity of a wave is proportional to the square of its amplitude ( $I \propto A^{2}$ ):

$I \propto 2 E_{0} cos (\frac{φ}{2})^{2}$

Answer: $∣2 E_{0} cos (φ /2) ∣^{2}$

Physics - Wave Optics Question with Solution | TestHub

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