Question

For what distance ray optics is a good approximation when the aperture is 2 mm wide and the wavelength is 200 nm?

• A. 20 m
• B. 30 m
• C. 50 m
• D. 40 m

Answer 1

The correct option is A

20 m

Step 1: Given data

Aperture width, $a=2mm$

Wavelength, $\lambda =200nm$

Step 2: Formula used

Fresnel distance, $Z_f=\frac{a^2}{\lambda }[wherea=apertureand\lambda =wavelength]$

Step 3: Calculating distance

Putting the value of aperture and wavelength in the Fresnel distance formula

$$\begin{gathered} Z_f=\frac{a^2}{\lambda } \\ {Z}_f=\frac{{(2\times {10}^{-3})}^2}{200\times {10}^{-9}}[1mm={10}^{-3}mand1nm={10}^{-9}m] \\ {Z}_f=20m \end{gathered}$$

Thus, $20m$ distance at which ray optics is a good approximation.

Hence, option A is the correct answer.