In interference experiment the path difference between two interfering waves at a point A on the screen is $\lambda / 3$, where $\lambda$ is the wavelength of these waves, and at another point B the path difference is $\lambda / 6$. The ratio of intensities at points A and B is ______.

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Wave Optics

In interference experiment the path difference between two interfering waves at a point A on the screen is

λ /3

, where

λ

is the wavelength of these waves, and at another point B the path difference is

λ /6

. The ratio of intensities at points A and B is ______.

Answer: (C)

For two equal sources the intensity at phase difference

Δ ϕ

I = 2 I_{0} (1 + cos Δ ϕ)

. A path difference

λ /3

gives

Δ ϕ_{A} = \frac{2 π}{λ} \cdot \frac{λ}{3} = \frac{2 π}{3}

, so

I_{A} = 2 I_{0} (1 + cos \frac{2 π}{3}) = 2 I_{0} (1 - \frac{1}{2}) = I_{0}

. A path difference

λ /6

gives

Δ ϕ_{B} = \frac{π}{3}

, so

I_{B} = 2 I_{0} (1 + cos \frac{π}{3}) = 2 I_{0} (1 + \frac{1}{2}) = 3 I_{0}

. The ratio of intensities is

\frac{I _{A}}{I _{B}} = \frac{1}{3}

JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Single correct option