Question

When the distance between source of light and screen is increased, then fringe width

• A. increases
• B. decreases
• C. remains same
• D. none of these

Hint:

To get wide, easily visible fringes, you should increase the screen distance (\(D\)) and use light with a longer wavelength (\(\lambda\)), while keeping the slit separation (\(d\)) small. This relationship \(\beta = \lambda D/d\) is fundamental to wave optics problems.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question relates to the interference of light, typically observed in an experiment like Young's Double-Slit Experiment (YDSE). Fringe width is the distance between two consecutive bright or dark fringes on the screen.
Step 2: Key Formula or Approach:
The formula for the fringe width (\(\beta\)) in a double-slit interference pattern is: \[ \beta = \frac{\lambda D}{d} \] where:
\(\lambda\) is the wavelength of the light used.
\(D\) is the distance between the slits (which act as the coherent sources) and the screen.
\(d\) is the distance between the two slits.
Step 3: Detailed Explanation:
The question states that the distance between the source of light (slits) and the screen is increased. This corresponds to an increase in the value of \(D\).
From the formula \(\beta = \frac{\lambda D}{d}\), we can see that the fringe width \(\beta\) is directly proportional to the distance \(D\), assuming \(\lambda\) and \(d\) are constant. \[ \beta \propto D \] Therefore, if \(D\) increases, the fringe width \(\beta\) will also increase. This means the bright and dark fringes on the screen will become more spread out.
Step 4: Final Answer:
Since the fringe width is directly proportional to the distance between the source and the screen, increasing this distance will cause the fringe width to increase. Option (A) is correct.