Question

In Young's double-slit experiment, if the width of $4$th bright fringe is $2\times {10}^{-2}cm$, then the width of $6$th bright fringe will be ____________ $cm$.

• A. $3\times {10}^{-2}$
• B. ${10}^{-2}$
• C. $2\times {10}^{-2}$
• D. $1.5\times {10}^{-2}$

Answer 1

The correct option is A $3\times {10}^{-2}$

Given, $x_1=2\times {10}^{-2}cm$
$m_1=4$th
$m_2=6$th, $x_2=$?
$\because x=m\frac{D\lambda }{d}$
$\therefore \frac{x_1}{x_2}=\frac{m_1}{m_2}$
$x_2=\frac{x_1\times m_2}{m_1}=\frac{2\times {10}^{-2}\times 6}{4}$
$=\frac{12\times {10}^{-2}}{4}=3\times {10}^{-2}cm$