Question

Two coherent sources P and Q produce interference at point A on the screen where there is a dark band which is formed between 4th bright band and 5th bright band. Wavelength of light used is 6000 Å. The path difference between PA and QA is ______.

Options

• 1.4 × 10^-4 cm

• 2.7 × 10^-4 cm

• 4.5 × 10^-4 cm

• 6.2 × 10^-4 cm

Answer 1

Two coherent sources P and Q produce interference at point A on the screen where there is a dark band which is formed between 4th bright band and 5th bright band. Wavelength of light used is 6000 Å. The path difference between PA and QA is 2.7 × 10^-4 cm.

Explanation:

As Δx = `(lambdadelta)/(2pi)`

[Where, Δx = path difference]

For 4th dark fringe,

δ = (2n + 1)π

⇒ δ = (2 × 4 + 1)π = 9π

 Δx = `(lambda.9pi)/(2pi)`

= `9/2`λ

= `9/2xx6xx10^-7`

= 2.7 × 10^-6 m

= 2.7 × 10^-4 cm