Question

Two coherent sources of wavelength \(\lambda\) produce steady interference pattern. The path difference corresponding to \(10^{\text{th}}\) order maximum will be

• A. 9.5\(\lambda\)
• B. 10.5\(\lambda\)
• C. 9\(\lambda\)
• D. 10\(\lambda\)

Hint:

For maxima: path difference = \(n\lambda\) (\(n = 0,1,2,\ldots\)). For minima: path difference = \((2n-1)\lambda/2\).

Answer 1

The Correct Option is D

Step 1: Understand the question.
Two coherent sources of wavelength $\lambda$ make an interference pattern. We need the path difference for the $10^{\text{th}}$ order bright fringe (maximum).
Step 2: Recall the condition for a maximum.
A bright fringe (constructive interference) happens when the path difference is a whole number of wavelengths: \[ \Delta = n\lambda, \] where $n$ is the order number $0, 1, 2, \dots$
Step 3: Identify the order.
The $10^{\text{th}}$ order maximum means $n = 10$.
Step 4: Plug in.
\[ \Delta = 10\lambda. \]
Step 5: Why a whole number.
For the two waves to arrive in step (crest meeting crest), one wave must travel an extra distance equal to an exact number of full wavelengths. For the 10th order that extra distance is exactly 10 wavelengths.
Step 6: State the answer.
The path difference is $10\lambda$. \[ \boxed{\Delta = 10\lambda} \]