InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A point source of monochromatic light is positioned in front of a zone plate at a distance a = 1.5 m from it. The image of the source is formed at a distance b = 1.0 m from the plate. Find the focal length of the zone plate. |
|
Answer» Solution :In a zone plate an undarkened circular disc is FOLLOWED by a number of altermetely undarkened and darkened rings. For the proper case, correspond to `1^(st), 2^(nd), 3^(rd)……` FRESNEL zones. LET `r_(1) =` radius of the central undarkened circle. Then for this to be first Fresnel zone in the present case, we must have `SL + LI - SL = lambda//2` Thus if `r_(1)` is the radius of the perphery of the first zone `sqrt(a^(2) + r_(1)^(2)) + sqrt(b^(2) + r_(1)^(2)) -(a + b) = (lambda)/(2)` or `(r_(1)^(2))/(2) ((1)/(a) + (1)/(b)) = (lambda)/(2)` or `(1)/(a) + (1)/(b) = (1)/(r_(1)^(2)//lambda)` It is clear that the plate is acting as a lens of focal length `f_(1) = (r_(1)^(2))/(lambda) = (ab)/(a+b) = 6`metre. This is the principle focal length. Other maxima are OBTAINED when `SL + LI - SI = 3(lambda)/(2), 5(lambda)/(2),..........` These focal lengths are ALSO `(r_(1)^(2))/(3lambda), (r_(1)^(2))/(5lambda),....` 
|
|