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:
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:
Show 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.
- 0.4 mm
- 0.1 mm
- 0.2 mm
- 0.5 mm
The Correct Option is C
Solution and Explanation
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
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