Question

In a double-slit experiment, the distance between the slits is 0.54 mm and the distance from the screen is 1.8m. If the distance between the adjacent maxima is 1.2 cm, then the wavelength of the light used in the experiment is:

• A. 800 nm
• B. 8000 nm
• C. 600 nm
• D. 5000 Å

Hint:

In double-slit diffraction, the wavelength can be found using the formula \( \lambda = \frac{y d}{L} \), where \( y \) is the distance between maxima, \( d \) is the slit separation, and \( L \) is the distance to the screen.

Answer 1

The Correct Option is C

Step 1: Using the double-slit diffraction formula.
The formula for the distance between adjacent maxima in a double-slit experiment is: \[ y = \frac{\lambda L}{d} \] where: - \( y \) is the distance between adjacent maxima, - \( L \) is the distance from the slits to the screen, - \( d \) is the distance between the slits, and - \( \lambda \) is the wavelength of the light.
Step 2: Applying the given values.
Given that \( y = 1.2 \, \text{cm} = 0.012 \, \text{m} \), \( L = 1.8 \, \text{m} \), and \( d = 0.54 \, \text{mm} = 0.54 \times 10^{-3} \, \text{m} \), we can rearrange the formula to solve for \( \lambda \): \[ \lambda = \frac{y d}{L} = \frac{0.012 \times 0.54 \times 10^{-3}}{1.8} \approx 600 \, \text{nm} \]
Step 3: Conclusion.
The wavelength of the light is 600 nm, so the correct answer is (C).