Question

Monochromatic light of 605 nm falls on a single slit of width 0.095 mm. The slit is located 85 cm from a screen. How far from the center is the first dark band?540 mm5,400 mm0.5 mm5.4 mm

Answer 1

The wavelength of the monochromatic beam is given as,

$\lambda=605\text{ nm}$

The value of the width of the slit is,

$d=0.095\text{ mm}$

The distance of the slit from the screen is,

$D=85\text{ cm}$

Thus, the distance of the dark band from the center is,

$y=\frac{(2m+1)\lambda D}{d}$

For the first dark band,

m=0,

Substituting all the known values,

The value of the distance of the dark band becomes,

$\begin{gathered} y=\frac{605\times10^{-9}\times85\times10^{-2}}{0.095\times10^{-3}} \\ y=540000\times10^{-8}\text{ m} \\ y=5.4\text{ mm} \end{gathered}$

Thus, the first dark band is 5.4 mm away from the center of the screen.

Hence, the correct answer is 5.4 mm.