Question

Light from a helium-neon laser $(\lambda =633\mathrm{nm})$passes through a circular aperture and is observed on a screen $4.0m$behind the aperture. The width of the central maximum is$2.5cm$. What is the diameter (in mm) of the hole?

Short answer

Diameter of the hole , D$=0.25mm$

Step-by-step solution

Helium-neon Laser

Because they're affordable and provides a relentless, visible output, helium-neon (He-Ne) lasers are commonly utilized for interferometry.

They typically work a wavelength of $633nm$, however customized versions with useable outputs at other visible and infrared wavelengths are available.

Find Distance 

In the circular-slit experiment, the formula for the width of the central fringe is

$w=\frac{2.44\lambda L}{D}$

We find diameter value using the above expression,

$D=\frac{2.44\lambda L}{w}$

Find Distance 

Distance is,

$D=\frac{2.44\lambda L}{w}$
$D=\frac{2.44\times 6.33\times {10}^{-7}m\times 4m}{2.5\times {10}^{-2}m}$

$=2.47\times {10}^{-4}m$

$=0.25\mathrm{mm}$