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 $4th$ zone for $\lambda_{1}$ coincides with the radius of 5$^{th}$ zone for $\lambda_{2}$. Then the ratio $\lambda_{1}:\lambda_{2}$ is
A) $\sqrt{4/5}$
B) $\sqrt{5/4}$
C) 5/4
D) 4/5
Explanation
(c) It is given that $r_{4} = \sqrt{4b\lambda_{1}}$ and $r_{5} = \sqrt{5b\lambda_{2}}$
are equal. Therefore $\sqrt{4b\lambda_{1}} = \sqrt{5b\lambda_{2}}$
Or $4b\lambda_{1} = 5b\lambda_{2}$
Or $\frac{\lambda_{1}}{\lambda_{2}} = \frac{5}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.