Question

In a Young's double slit experiment, the slits are separated by 0.2 mm and placed 2.0 m away. The distance between the central bright fringe and the first bright fringe (fringe width) is measured to be 1.5 cm. Determine the wavelength of light used in the experiment.

• A. 4200 Å
• B. 5000 Å
• C. 4600 Å
• D. 15000 Å (Calculated result)

Hint:

Always ensure your units are consistent. Convert mm and cm to meters (\textbf{m}) before plugging them into the formula to avoid power-of-ten errors.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In Young's Double Slit Experiment (YDSE), the distance between consecutive bright fringes (fringe width $\beta$) is given by the formula $\beta = \frac{\lambda D}{d}$.
Step 2: Calculation:
Given: $d = 0.2\text{ mm} = 0.2 \times 10^{-3}\text{ m}$, $D = 2.0\text{ m}$, $\beta = 1.5\text{ cm} = 1.5 \times 10^{-2}\text{ m}$. $$\lambda = \frac{\beta \times d}{D}$$ $$\lambda = \frac{(1.5 \times 10^{-2}) \times (0.2 \times 10^{-3})}{2.0}$$ $$\lambda = \frac{0.3 \times 10^{-5}}{2.0} = 0.15 \times 10^{-5}\text{ m} = 1500 \times 10^{-9}\text{ m} = 15000\text{ \AA}$$
Step 3: Final Answer:
The calculated wavelength is 15000 \AA.