Question

White light is passed through the double slit and interference pattern is observed on a screen $2.5\text{m}$ away. The separation between the slits is $0.5\text{mm}$. The first violet and red fringes are formed at distances of $2\text{mm}$ and $3.5\text{mm}$ away from the central white fringe respectively. Calculate wavelengths of red and violet light.

• A. $800\text{nm}$ and $400\text{nm}$
• B. $350\text{nm}$ and $200\text{nm}$
• C. $750\text{nm}$ and $350\text{nm}$
• D. $700\text{nm}$ and $400\text{nm}$

Answer 1

The correct option is D $700\text{nm}$ and $400\text{nm}$

Given:
$D=2.5\text{m}$
$d=0.5\text{mm}$

For the first bright fringe, the distance from the center is,
$\beta =\frac{D\lambda }{d}$

For violet light,
$\beta =2\text{mm}$
Thus, $2\times {10}^{-3}=\frac{2.5\times {\lambda }_v}{0.5\times {10}^{-3}}$
$\Rightarrow {\lambda }_v=\frac{2}{5}\times {10}^{-6}\text{m}=400\text{nm}$

Similarly for red light,
$\beta =3.5\text{mm}$
Thus, $3.5\times {10}^{-3}=\frac{2.5\times {\lambda }_r}{0.5\times {10}^{-3}}$

${\lambda }_r=0.7\times {10}^{-6}\text{m}=700\text{nm}$

Hence, $\left(D\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question :}\\ \text{Application: The double slit experiment can be used}\\ \text{to determine the wavelength of visible light.}\end{array}$