First slide

Young's double slit Experiment

Question

In the Young's double slit experiment, the intensity of light at a point on the screen where the path difference $λ$ . is K, ( $λ$ . being the wavelength of light used). The intensity at a point where the path difference is $λ$ /4 will be

Moderate

A

K
B

K/4
C

K/2
D

zero

Solution

Intensity at any point on the screen is
$I = 4 I_{0} \cos^{2} \frac{ϕ}{2}$
where $I_{0}$ is the intensity of either wave and $ϕ$ is the phase different between two waves.
Phase difference, $ϕ = \frac{2 π}{λ} \times$ path difference
When path difference is $λ$ , then
$ϕ = \frac{2 π}{λ} \times λ = 2 π$
$∴ I = 4 I_{0} \cos^{2} (\frac{2 π}{2}) = 4 I_{0} \cos^{2} (π) = 4 I_{0} = K$ . . . . .(i)
$When path difference is \frac{λ}{4}, then$
$ϕ = \frac{2 π}{λ} \times \frac{λ}{4} = \frac{π}{2}$
$∴ I = 4 I_{0} \cos^{2} (\frac{π}{4}) = 2 I_{0} = \frac{K}{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App