Question

You want to photograph a circular diffraction pattern whose central maximum has a diameter of $1.0cm$. You have a helium neon laser $(\lambda =633\mathrm{nm})$and a$0.12-mm$-diameter pinhole. How far behind the pinhole should you place the screen that’s to be photographed?

Short answer

Distance for the screen to be photographed, $d$$=0.777m$

Step-by-step solution

Aperture Diffraction

When light passes through a narrow opening, such as an aperture with a low f-number, it causes lens diffraction, which is an optical interference.

When the wavelength of light and the size of the opening are about the same, lens diffraction occurs.

Find the distance 

In the aperture diffraction experiment, the center width is given by,

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

We can find$L$by solving parametrically.

$L=\frac{wD}{2.44\lambda }$

Find the distance 

This will be the length in our situation.

$L=\frac{wD}{2.44\lambda }$

localid="1650215739018" $L=\frac{1\times {10}^{-2}m\times 1.2\times {10}^{-4}m}{2.44\times 6.33\times {10}^{-7}m}$

$=0.777\mathrm{m}$