Two identical light waves, propagating in the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the intensity of each individual wave be $I_0$. When two waves with the same frequency and amplitude superpose, the resultant intensity $I$ is

Vedclass · Accepted Answer

$\cos ^2(\delta / 2)$

Vedclass · Answer

(C) Let the intensity of each individual wave be $I_0$. When two waves with the same frequency and amplitude superpose, the resultant intensity $I$ is given by the formula: $I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \delta$ Since the waves are identical, $I_1 = I_2 = I_0$. Substituting these values: $I = I_0 + I_0 + 2\sqrt{I_0 I_0} \cos \delta$ $I = 2I_0 + 2I_0 \cos \delta$ $I = 2I_0 (1 + \cos \delta)$ Using the trigonometric identity $1 + \cos \delta = 2 \cos^2(\delta / 2)$: $I = 2I_0 (2 \cos^2(\delta / 2))$ $I = 4I_0 \cos^2(\delta / 2)$ Therefore, the resultant intensity is proportional to $\cos^2(\delta / 2)$.

Two identical light waves, propagating in the same direction, have a phase difference $\delta$. After they superpose, the intensity of the resulting wave will be proportional to

Similar Questions

Path difference between two light waves at a point $P$ for constructive interference will be

Two point sources $X$ and $Y$ emit waves of the same frequency and speed,but $Y$ lags in phase behind $X$ by $2\pi l$ radians. If there is a maximum in direction $D$,the distance $XO$ (where $n$ is an integer) is given by:

Light exhibits wave nature because...

In the phenomenon of interference :-
$(a)$ Total energy is conserved
$(b)$ Total energy is not conserved
$(c)$ Only bright fringes are formed
$(d)$ The frequency of two sources is equal

Which characteristic of light determines its color?

Vedclass Test Series

Exam Paper Generator

Online Exam Module