Question

Interference fringes are observed on a screen by illuminating two thin slits $1mm$ apart with a light source.

• A. $2.05\mu m$
• B. $2.87nm$
• C. $2nm$
• D. $1.27\mu m$

Answer 1

The correct option is D

$1.27\mu m$

Solution:

Step 1: Given information

Distance between two slits$=1mm$

$\lambda =632.8nm$

$D=100cm$

$y=1.27mm$

Step 2: Calculate the distance between interference fringes

Given, d $=1mm$, $\lambda =632.8nm$, $D=100cm$, $y=1.27mm$, $\Delta x=d\sin \theta$$(\theta =small)$, and $\Delta x=d\tan \theta$

$$\begin{gathered} \Rightarrow \Delta x=\frac{dy}{D} \\ \Rightarrow \Delta x=\frac{1\times {10}^{-3}\times 1.27\times {10}^{-3}}{100\times {10}^{-3}} \end{gathered}$$

$=1.27\times 10{}^{-6}m$

$=1.27\mu m$

Hence, the correct option is (D).