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

In Young’s double slit experiment, the condition for the first minimum is given by:

a \sin \theta = m \lambda

Where:

• a is the slit separation.
• \theta is the angle of the first minimum.
• m is the order of the minimum (for first minimum, m = 1).
• \lambda is the wavelength of light used.

Given:

• \lambda = 800 \, \text{nm} = 800 \times 10^{-9} \, \text{m}
• m = 1
• At the first minimum, \theta is small, hence \sin \theta \approx \theta (in radians), and the path difference \approx \lambda.

Thus, the equation simplifies to:

a \sin \theta = \lambda

Assuming normal incidence and small angles, \theta \approx 0, which simplifies to:

a = \lambda

Plug in the values:

a = 800 \times 10^{-9} \, \text{m} = 0.2 \, \text{mm}

Therefore, the slit separation a is 0.2 mm.

Among the given options, the correct answer is 0.2 mm.