Question

FIGURE P33.56 shows the light intensity on a screen behind a circular aperture. The wavelength of the light is $500\mathrm{nm}$and the screen is $1.0\mathrm{m}$behind the slit. What is the diameter (in mm) of the aperture?

Short answer

The diameter of the aperture$0.12\mathrm{mm}$

Step-by-step solution

Circular Aperture

We can see by the graph that the center fringe of this circular aperture trial is $1$cm. Like a result, the aperture width can be given in terms:

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

Aperture Diameter

We will have aperture diameter

$$\begin{gathered} D=\frac{2.44\cdot 5\times {10}^{-7}\times 1m}{1\times {10}^{-2}} \\ =1.22\times {10}^{-4}\mathrm{m} \\ =0.12\mathrm{mm} \end{gathered}$$