Question

In a Young’s double slit experiment, two slits are illuminated with light of wavelength \(800 \, \text{nm}\). The first minimum is detected at \(P\). The value of slit separation \(a\) is:

• A. 0.4 mm
• B. 0.1 mm
• C. 0.2 mm
• D. 0.5 mm

Hint:

For Young’s double-slit experiments:
• Use the condition for minima or maxima to relate wavelength, slit separation, and screen distance.
• Ensure units are consistent when calculating.

Answer 1

The Correct Option is C

Condition for Minima: Path difference for the first minimum:

\[ \Delta x = \frac{\lambda}{2}. \]

Slit Separation: From geometry:

\[ a = \frac{\lambda D}{\Delta x}. \]

Substituting values:

\[ a = \frac{800 \times 10^{-9} \times 5 \times 10^{-2}}{0.5 \times 10^{-3}} = 0.2 \, \text{mm}. \]

Final Answer: 0.2 mm