Question

Determine the Fresnel distance if the aperture is of the size $1\mathrm{cm}$ and the wavelength is $500\mathrm{nm}$.

Answer 1

Step 1: Given data

The wavelength of the light, $\mathrm{\lambda }=500\mathrm{nm}=500\times {10}^{-9}\mathrm{m}$

Size of aperture, $\mathrm{a}=1\mathrm{cm}=1\times {10}^{-2}\mathrm{m}$

Step 2: Formula used

Fresnel distance is the distance of the screen from the slit so that the spreading of light due to diffraction from the center of the screen is just equal to the size of the slit. It is denoted by Z_F.

${\mathrm{Z}}_{\mathrm{F}}=\frac{{\mathrm{a}}^2}{\mathrm{\lambda }}$

Here,

$\mathrm{a}$ is the size of the aperture.

$\text{λ}$ is the wavelength of light.

Step 3: Calculation

By substituting the given values in the above formula, we get

$$\begin{gathered} {\mathrm{Z}}_{\mathrm{F}}=\frac{{(1\times {10}^{-2})}^2}{500\times {10}^{-9}} \\ =200\mathrm{m} \end{gathered}$$

Hence, the Fresnel distance will be $Z_F=200\text{m}$.