Question

A beam of light of wavelength $600\mathrm{nm}$ from a distance source falls on a single slit $1\mathrm{mm}$ wide and a resulting diffraction pattern is observed on a screen $2\mathrm{m}$ away. The distance between the first dark fringes on either side of central bright fringe is

• A. $1.2\mathrm{cm}$
• B. $1.2\mathrm{mm}$
• C. $2.4\mathrm{mm}$
• D. $2.4\mathrm{cm}$

Answer 1

The correct option is C

$2.4\mathrm{mm}$

Step 1: Given data

Wavelength of a light, $\mathrm{\lambda }=600\mathrm{nm}=600\times {10}^{-9}\mathrm{m}$

Width of a slit, $\mathrm{d}=1.0\mathrm{mm}={10}^{-3}\mathrm{m}$

Distance between screen and slit, $\mathrm{D}=2\mathrm{m}$

For first dark fringe, $\mathrm{n}=1$

Let the distance between the central fringe and first dark fringe on one side$=\mathrm{y}$

Step 2: Calculating the distance between first dark fringes on either side of central bright fringe

The formula to calculate the distance between the first fringe and the central bright fringe is given below,

$$\begin{gathered} \mathrm{y}=\mathrm{n}\frac{\mathrm{\lambda D}}{\mathrm{d}} \\ \Rightarrow \mathrm{y}=1\times \frac{600\times {10}^{-9}\mathrm{m}\times 2\mathrm{m}}{{10}^{-3}\mathrm{m}} \\ \Rightarrow \mathrm{y}=1.2\times {10}^{-3}\mathrm{m} \\ \Rightarrow \mathrm{y}=1.2\mathrm{mm} \end{gathered}$$

Therefore the total distance between the first dark fringes on either side of central bright fringe is $2\mathrm{y}=2\times 1.2\mathrm{mm}=2.4\mathrm{mm}$

Hence, option (C) is the correct answer.