Question

Light from a helium-neon laser $(\lambda =633\mathrm{nm})$illuminates a circular aperture. It is noted that the diameter of the central maximum on a screen $50\mathrm{cm}$behind the aperture matches the diameter of the geometric image. What is the aperture's diameter (in mm)?

Short answer

The aperture's diameter$0.88\mathrm{mm}$

Step-by-step solution

Circular Aperture

When combining wavelength and aperture diameter D, the size of the girder emerging out of a circular- lens thought experiment at range L out from lens aperture is given by

$w=\frac{2\times 44\times \lambda L}{D}$

Diameter

Knowing as w=D, the girth can be given as,

$$\begin{gathered} D^2=2\times 44\times \lambda L \\ \Rightarrow D=\sqrt{2\times 44\times \lambda L} \end{gathered}$$

$$\begin{gathered} D=\sqrt{2.44\times 6.33\times {10}^{-7}m\times 0.5m} \\ =8.79\times {10}^{-4}\mathrm{m} \\ =0.88\mathrm{mm} \end{gathered}$$