Young’s Double Slit Experiment
Question: In a Young’s double slit experiment the two slits are separated by \(d = 1\,\text{mm}\) and the screen is placed at a distance \(L = 1\,\text{m}\) from the slits. When light of wavelength \(\lambda = 600\,\text{nm}\) is used, what is the fringe separation on the screen?
- (1) \(3\,\text{mm}\)
- (2) \(0.30\,\text{mm}\)
- (3) \(0.60\,\text{mm}\)
- (4) \(6\,\text{mm}\)
Select the Correct Option
Step‑by‑Step Explanation
Step 1: Write the Formula
The fringe separation \(\Delta y\) in Young’s double slit experiment is given by:
\[
\Delta y = \frac{\lambda L}{d},
\]
where \(\lambda\) is the wavelength, \(L\) is the distance from the slits to the screen, and \(d\) is the slit separation.
Step 2: Substitute the Given Values
Here, \(\lambda = 600\,\text{nm} = 600 \times 10^{-9}\,\text{m}\), \(L = 1\,\text{m}\), and \(d = 1\,\text{mm} = 1 \times 10^{-3}\,\text{m}\). Substituting these into the formula:
\[
\Delta y = \frac{600 \times 10^{-9}\,\text{m} \times 1\,\text{m}}{1 \times 10^{-3}\,\text{m}}.
\]
Step 3: Simplify the Expression
\[
\Delta y = \frac{600 \times 10^{-9}}{10^{-3}} = 600 \times 10^{-6}\,\text{m} = 0.6 \times 10^{-3}\,\text{m} = 0.60\,\text{mm}.
\]
Final Answer: The fringe separation is \(0.60\,\text{mm}\), which corresponds to option (3).
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