Question

In Young's experiment, using red light ($\lambda = 6600$ \AA), 60 fringes are seen in the field of view. How many fringes will be seen by using violet light ($\lambda = 4400$ A)?

• A. 10
• B. 20
• C. 45
• D. 90

Hint:

Number of fringes \(\propto \dfrac{1}{\lambda}\). A smaller wavelength (violet) gives more fringes in the same field of view.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
In Young's double slit experiment, the fringe width is given by \(\beta = \dfrac{\lambda D}{d}\). The number of fringes visible in a given field of view is inversely proportional to the fringe width, hence inversely proportional to the wavelength.
Step 2: Detailed Explanation:
If \(n_1\) fringes are seen with wavelength \(\lambda_1\) and \(n_2\) fringes with \(\lambda_2\), then: \[ n_1 \lambda_1 = n_2 \lambda_2 \] \[ 60 \times 6600 = n_2 \times 4400 \] \[ n_2 = \frac{60 \times 6600}{4400} = 90 \]
Step 3: Final Answer:
The number of fringes seen with violet light is 90.