Question

An object illuminated by 5000 Å wavelength of light is placed at 60 cm from a zone plate & its image (brightness) is obtained at 30 cm from the plate. Calculate the number of Fresnel zones in a radius of 5 cm of the plate –
1. 20000
2. 25000
3. 15000
4. None

Answer 1

Correct Answer - Option 2 : 25000

For zone plate,

\(\frac{1}{v}\; + \;\frac{1}{u} = \frac{1}{{{f_n}}};{f_n} = \frac{{r_n^2}}{{n\lambda }}\) 

Here, u = object distance = 60 cm

v = image distance = 30 cm

λ = wavelength = 5000 × 10^-8 cm

r_n = Radius for the nth ring of the zone plate = 5 cm

Now, \(\frac{1}{{{f_n}}} = \frac{1}{{30}}\; + \;\frac{1}{{60}}\)

\(\Rightarrow {f_n} = 20 = \frac{{{5^2}}}{{n \times 5000 \times {{10}^{ - 8}}}}\) 

⇒ n = 25000