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: Understanding the Concept:
Intensity from two equal sources is \(I = 4I_0\cos^2\dfrac\phi2\), where \(\phi = \dfrac{2\pi}{\lambda}\Delta x\).

Step 2: Path difference zero:
\(\phi = 0\), so \(I_1 = 4I_0\cos^20 = 4I_0\).

Step 3: Path difference \(\lambda/4\):
\(\phi = \dfrac{2\pi}\lambda\cdot\dfrac\lambda4 = \dfrac\pi2\), so \(I_2 = 4I_0\cos^2\dfrac\pi4 = 4I_0\cdot\dfrac12 = 2I_0\).

Step 4: Ratio:
\[ I_1 : I_2 = 4I_0 : 2I_0 = 2 : 1 \]
Option (B).

Final Answer:
I1 = 4 I0 and I2 = 2 I0, a ratio of 2 to 1. \[ \boxed{\text{(B) }2:1} \]