Question

In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the slits, If the screen is moved by $5\times {10}^{-2}$ m towards the slits, the change in fringe width is $3\times {10}^{-5}$ m. If separation between the slits is ${10}^{-3}$ m, the wavelength of light used is

• A. $6000\mathring{A}$
• B. $5000\mathring{A}$
• C. $3000\mathring{A}$
• D. $4500\mathring{A}$

Answer 1

The correct option is A $6000\mathring{A}$

A and B are slits

String width, $B=\frac{D\lambda }{d}$

$\lambda =\left(\frac{Bd}{D}\right)$

$B_1=\frac{D_1\lambda }{d}$

$B_2=\frac{D_2\lambda }{d}$

$\Rightarrow (B_1-B_2)=(D_1-D_2)\frac{\lambda }{d}$

$\Rightarrow 3\times {10}^{-5}=5\times {10}^{-2}\times \frac{\lambda }{{10}^{-3}}$

$\Rightarrow \lambda =\left(\frac{3\times {10}^{-5}\times {10}^{-3}}{5\times {10}^{-2}}\right)$

$=\frac{3}{5}\times {10}^{-8+2}=0.6\times {10}^{-6}$

$=6\times {10}^{-7}m=6000\dot{A}$