Question

Graph shows variation of fringe width (X) versus distance of the screen (D) in Young's experiment. The wavelength $\lambda$ is:

• A. slope $\times d^2$
• B. $d/\text{slope}$
• C. $\text{slope}/d$
• D. slope $\times d$

Hint:

In $X = \frac{\lambda D}{d}$, $X$ is directly proportional to $D$.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to relate the physical quantities in YDSE to the slope of a specific graph.

Step 2: Key Formula or Approach:
Fringe width \( X = \frac{\lambda D}{d} \).

Step 3: Detailed Explanation:
In the graph, \( X \) is on the y-axis and \( D \) is on the x-axis.
Rewriting the formula as \( y = mx \):
\[ X = \left( \frac{\lambda}{d} \right) D \]
The slope of the graph is given by the coefficient of \( D \):
\[ \text{slope} = \frac{\lambda}{d} \]
To find wavelength \( \lambda \):
\[ \lambda = \text{slope} \times d \]

Step 4: Final Answer:
Wavelength is calculated as \( \text{slope} \times d \).