First slide

Coherent sources

Question

In the diagram shown, S is a source of light emitting plane polarized light with plane of polarization parallel to the plane of the figure having wavelength $λ$ . M is a perfectly reflecting plane mirror. Intensity of light emitted by the source S is I₀. If SM = MP = SP = N $λ$ where N = 10⁶, then intensity of light at P is

Difficult

A

4 I₀
B

3 I₀
C

2 I₀
D

I₀

Solution

Due to reflection at the mirror M, the reflected ray suffers an additional phase difference of 180^o which is equivalent to a path difference of $\frac{λ}{2}$ . So total path difference at P
$= \{(SM + MP) - SP\} + \frac{λ}{2} = 10^{6} λ + \frac{λ}{2}$ . Hence the waves interfering at P has a phase difference of 180^o. Therefore the angle between the electric fields at P is 120^o as shown in the figure.
$\begin{array}{l} ∴ E_{R} = E_{0} \cos 60^{o} + E_{0} \cos 60^{o} = E_{0} \\ ∴ \frac{I_{R}}{I_{0}} = {(\frac{E_{R}}{E_{0}})}^{2} = 1 \Rightarrow I_{R} = I_{0} \end{array}$

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