Question

In a Young's double slit experiment, the slits are separated by \(0.28\,\text{mm}\) and the screen is placed \(1.4\,\text{m}\) away from the slits. The distance between the central bright fringe and the \(4^{\text{th}}\) order bright fringe is measured to be \(1.2\,\text{cm}\). The wavelength of light used in this experiment is

• A. \(2400\,\text{nm}\)
• B. \(600\,\text{nm}\)
• C. \(1200\,\text{nm}\)
• D. \(800\,\text{nm}\)

Hint:

In Young's double slit experiment, the position of the \(n^{\text{th}}\) bright fringe is \[ y_n=\frac{n\lambda D}{d}. \] Always convert all given quantities into SI units before substitution.

Answer 1

The Correct Option is B

Step 1: Write fringe position formula.
y_n = nλD/d. Rearranging: λ = (y_n × d)/(n × D).

Step 2: Substitute given data.
λ = (1.2×10⁻² × 0.28×10⁻³)/(4 × 1.4) = 0.336×10⁻⁵/5.6 = 6×10⁻⁷ m.

Step 3: Convert to nanometers.
6×10⁻⁷ m = 600 nm.

Step 4: Final Answer:
600 nm.