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Q.

In a Fresnel’s diffraction arrangement, the screen is at a distance of 2 meter from a circular aperture. It is found that for light of wavelengths λ1  and λ2,  the radius of 4th  zone for λ1  coincides with the radius of  5th zone for λ2. Then the ratio λ1:λ2  is

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a

4/5

b

5/4

c

5/4

d

4/5

answer is C.

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Detailed Solution

It is given that r4=4bλ1  and  r5=5bλ2 are equal.  Therefore  4bλ1=5bλ2  or  4bλ1=5bλ2   or  λ1λ2=54.
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In a Fresnel’s diffraction arrangement, the screen is at a distance of 2 meter from a circular aperture. It is found that for light of wavelengths λ1  and λ2,  the radius of 4th  zone for λ1  coincides with the radius of  5th zone for λ2. Then the ratio λ1:λ2  is