Question

When monochromatic light of wavelength \(600\;nm\) is used in Young's double slit experiment, the fifth order bright fringe is formed at \(6\;mm\) from the central bright fringe on the screen. If the experiment is conducted with light of wavelength \(400\;nm\), then the third order bright fringe will be located at

• A. \(1.6\;mm\)
• B. \(2\;mm\)
• C. \(2.4\;mm\)
• D. \(3\;mm\)

Hint:

In Young's double slit experiment, \[ y_n=n\beta \] and fringe width \(\beta\) is directly proportional to wavelength.

Answer 1

The Correct Option is C

Step 1: Use the fringe position formula.
In Young's double slit experiment, position of the \(n^{th}\) bright fringe is \[ y_n=n\beta \] where \[ \beta=\frac{\lambda D}{d} \] is the fringe width.

Step 2: Find the fringe width for wavelength \(600\;nm\).
Given, \[ y_5=6\;mm \] So, \[ 5\beta_1=6 \] \[ \beta_1=\frac{6}{5} \] \[ \beta_1=1.2\;mm \]

Step 3: Find the new fringe width for wavelength \(400\;nm\).
Fringe width is directly proportional to wavelength: \[ \beta\propto \lambda \] Therefore, \[ \frac{\beta_2}{\beta_1}=\frac{400}{600} \] \[ \beta_2=1.2\times \frac{2}{3} \] \[ \beta_2=0.8\;mm \]

Step 4: Find the position of the third bright fringe.
For third order bright fringe, \[ y_3=3\beta_2 \] \[ y_3=3\times 0.8 \] \[ y_3=2.4\;mm \]

Step 5: Final conclusion.
Hence, the third order bright fringe will be located at \[ \boxed{2.4\;mm} \]