Question

The third focal distance of the zone plate for a light of wavelength λ and the n_th angle radius r_n is-
1. \(\frac{{r_n^2}}{{3n\lambda }}\)
2. \(\frac{{r_n^2}}{{7n\lambda }}\)
3. \(\frac{{r_n^2}}{{5n\lambda }}\)
4. \(\frac{{r_n^2}}{{n\lambda }}\)

Answer 1

Correct Answer - Option 3 : \(\frac{{r_n^2}}{{5n\lambda }}\)

Concept:

Zone Plate:

A zone plate is a device used to focus light by using its wave characters like diffraction. 

It is different from other lenses as it uses diffraction instead of refraction. 

It is also known as Fresnel zone plates in honour of Augustin-Jean Fresnel.

The focal length for zonal plate is given as

\(f = \frac{(r_n)^2}{(2p-1)n λ }\)

p is number of focal length, rn is radius of plate, λ is wavelength. 

Calculation:

For 3rd focal length, p = 3, 

then the focal length will be

\(f = \frac{{r_n^2}}{{(2 \times 3 -1)n\lambda }}\)

\(\implies f = \frac{{r_n^2}}{{5n\lambda }}\)

So, the correct option is \(\frac{{r_n^2}}{{5n\lambda }}\)