Question

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

• A. $\sqrt{4/5}$
• B. $\sqrt{5/4}$
• C. $5/4$
• D. $4/5$

Answer 1

Answer: (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 $\frac{{\lambda }_1}{{\lambda }_2}=\frac{5}{4}$