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: Formula
Fringe width $X = \frac{\lambda D}{d}$.

Step 2: Analysis
In a graph of $X$ (y-axis) vs $D$ (x-axis), the equation is of the form $y = mx$.
Comparing $X = (\frac{\lambda}{d})D$ with $y = mx$, the slope $m = \frac{\lambda}{d}$.

Step 3: Calculation
Slope $= \lambda / d \implies \lambda = \text{slope} \times d$.

Step 4: Conclusion
Hence, the wavelength is calculated as slope $\times d$. Final Answer: (D)