Which of the following statements are correct when white light is incident on a zone plate from a point?a)The foci of higher wavelength are nearer to the zone plate.b)The nearest focus from the zone plate is of the highest intensity.c)The foci of lower wavelengths are nearer to the zone plate.d)For a particular wavelength, a number of foci are formed.Correct answer is option 'A,B'. Can you explain this answer?

Question

Answer

The radius of zone plate

where b = distance of point from zone plate
⇒ r ∝ √n
focus f

=> focal length =>

Hence, first statements is true.
The highest intensity occurs at a point for which zone plate is produced. => (iv) statement is wrong for a particular wavelength a number of foci are formed, and (iii) statement is wrong.
Thus, statements (i) and (ii) are right.

Answer

Statement a: The foci of higher wavelength are nearer to the zone plate.

This statement is correct. A zone plate is a circular aperture with alternating transparent and opaque zones. When white light is incident on a zone plate from a point source, the different wavelengths of light will diffract differently. The zones act as a diffraction grating, causing the different colors (wavelengths) to focus at different distances from the zone plate. The longer wavelengths (such as red) will focus at a closer distance to the zone plate compared to the shorter wavelengths (such as blue). Therefore, the foci of higher wavelength are indeed nearer to the zone plate.

Statement b: The nearest focus from the zone plate is of the highest intensity.

This statement is also correct. The intensity of the focused light depends on the diffraction efficiency of the zone plate. The diffraction efficiency is higher for the first-order foci compared to higher-order foci. Therefore, the nearest focus, which corresponds to the first-order diffraction, will have the highest intensity.

Statement c: The foci of lower wavelengths are nearer to the zone plate.

This statement is incorrect. As mentioned earlier, the foci of lower wavelengths (such as blue) are actually farther away from the zone plate compared to the foci of higher wavelengths (such as red).

Statement d: For a particular wavelength, a number of foci are formed.

This statement is incorrect. For a particular wavelength, only one focus is formed by the zone plate. The zone plate acts as a lens for each specific wavelength, focusing the light at a single point. However, different wavelengths will have different focal points, resulting in multiple foci for a range of wavelengths (as described in statement a).

In summary, statements a and b are correct, while statements c and d are incorrect. The foci of higher wavelength are nearer to the zone plate, and the nearest focus from the zone plate is of the highest intensity.

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