Question

In a Young’s double-slit experiment, two light waves, each of intensity I₀, interfere at a point, having a path difference `lambda/8` on the screen. Find the intensity at this point.

Answer 1

Given: Intensity of each wave (I₀)

Path difference (Δx) = `lambda/8`

Formula: The resultant intensity in an interference pattern is given by:

I = `I_1 + I_2 + sqrt(2I_1I_2 cos phi)`

Since both waves have equal intensity,

I₁ = I₂ = I₀

The equation simplifies to:

I = `I_0(2 + sqrt 2)`

Where the phase difference Φ is related to the path difference by:

Φ = `(2 pi)/lambda xx Delta x`

Substituting Δx = `lambda/8`

Φ = `(2 pi)/pi xx lambda/8`

= `(2 pi)/8`

= `pi/8`

Then,

I = `2I_0(1 + sqrt 2/2)`

= `I_0(2 + sqrt 2)`