Question

The ratio of intensities at two points on the screen in Young's double slit experiment when waves from the two slits have a path difference of zero and \(λ/4\) is (\(λ\) is the wavelength of light used) (\(cos0^{\circ} = 1\), \(cosπ/2 = 0\))

• A. \(1:2\)
• B. \(2:1\)
• C. \(1:4\)
• D. \(4:1\)

Hint:

Phase difference is 2 pi over lambda times path difference; intensity goes as cos squared of half the phase.

Answer 1

The Correct Option is B

Step 1: Use the phase directly:
$I\propto\cos^2(\phi/2)$.

Step 2: Evaluate:
For $\phi = 0$: $\cos^2 0 = 1$. For $\phi = \pi/2$: $\cos^2(\pi/4) = \tfrac12$.

Step 3: Ratio:
$1 : \tfrac12 = 2 : 1$, option (B).

Final Answer:
The intensity ratio is 2 : 1. \[ \boxed{\text{(B) }2:1} \]