1. Tardigrade
  2. Question
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  4. 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 4 th zone for λ1 coincides with the radius of 5 text th zone for λ2. Then the ratio λ1: λ2 is

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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 $\lambda_{1}$ and $\lambda_{2}$, the radius of $4$ th zone for $\lambda_{1}$ coincides with the radius of $5^{\text {th }}$ zone for $\lambda_{2}$. Then the ratio $\lambda_{1}: \lambda_{2}$ is

Wave Optics

Solution:

It is given that $r_{4}=\sqrt{4 b \lambda_{1}}$
and $r_{5}=\sqrt{5 b \lambda_{2}}$ are equal.
Therefore $\sqrt{4 b \lambda_{1}}=\sqrt{5 b \lambda_{2}}$
or $4 b \lambda_{1}=5 b \lambda_{2}$
or $\frac{\lambda_{1}}{\lambda_{2}}=\frac{5}{4}$