JEE PYQ: Wave Optics Question 22
Question 22 - 2020 (08 Jan Shift 2)
In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is $\frac{1}{8}$th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is:
(1) 0.853
(2) 0.672
(3) 0.568
(4) 0.760
Show Answer
Answer: (1)
Solution
Given, Path difference, $\Delta x = \frac{\lambda}{8}$
Phase difference, $\Delta\phi = \frac{2\pi}{\lambda}\Delta x$
$= \frac{2\pi}{\lambda} \times \frac{\lambda}{8} = \frac{\pi}{4}$
$I = I_0\cos^2\left(\frac{\Delta\phi}{2}\right)$
$\Rightarrow \frac{I}{I_0} = \cos^2\left(\frac{\pi/4}{2}\right) = \cos^2\left(\frac{\pi}{8}\right)$
$\Rightarrow \frac{I}{I_0} = 0.853$
BETA
