Question

A fringe width of $6\text{mm}$ was produced for two slits separated by $1\text{mm}$. The screen is placed $10\text{m}$ away. The wavelength of light used is ${}^{\prime }{x}^{\prime }\text{nm}$. The value of ${}^{\prime }{x}^{\prime }$ to the nearest integer is

Answer 1

Given data: $\beta =6\text{mm},d=1\text{mm},D=10\text{m}$
We have to find wavelength of the light used $\lambda =?$

We know that fringe width is related to wavelength as
$\beta =\frac{\lambda D}{d}$
$6\times {10}^{-3}=\frac{\lambda \times 10}{1\times {10}^{-3}}$
$\Rightarrow \lambda =\frac{6\times {10}^{-3}\times 1\times {10}^{-3}}{10}=600\times {10}^{-9}\text{m}$
$\Rightarrow \lambda =600\text{nm}$
$\therefore 600$ is the required value.