In a Young's double-slit experiment, the time-averaged value of $\cos ^ { 2 } \left( \omega t - 2 \pi r _ { 0 } / \lambda \right)$, where $r _ { 0 }$ is the distance from the center of the slits to the point of interest, and $\lambda$ is the wavelength of light, is
A) 0
B) 1/2.
C) $r _ { 0 } / \lambda .$
D) $1 / \sqrt { 2 }$

Question

Quizplus · Accepted Answer

The time-averaged value of a squared cosine function, such as $\cos^2(x)$, over a complete cycle is 1/2. This is a standard result from trigonometry and does not depend on the specific form of the argument of the cosine function.

In a Young's Double-Slit Experiment, the Time-Averaged Value Of cos⁡2(ωt−2πr0/λ)\cos ^ { 2 } \left( \omega t - 2 \pi r _ { 0 } / \lambda \right)cos2(ωt−2πr0​/λ)

In a Young's Double-Slit Experiment, the Time-Averaged Value Of $\cos ^ { 2 } \left( \omega t - 2 \pi r _ { 0 } / \lambda \right)$