Question

In the far field diffraction pattern of a single slit under polychromatic illumination, the first minimum with the wavelength ${\lambda }_1$ is found to be coincident with the third maximum at ${\lambda }_2$. Then, which of the following equality is true?

• A. $3{\lambda }_1=0.3{\lambda }_2$
• B. $3{\lambda }_1={\lambda }_2$
• C. ${\lambda }_1=3.5{\lambda }_2$
• D. $0.3{\lambda }_1=3{\lambda }_2$

Answer 1

The correct option is C ${\lambda }_1=3.5{\lambda }_2$

Position of first minima = position of third maxima
i.e.,
$\frac{1\times {\lambda }_{1}D}{d}=\frac{\left(}{2\times 3+1}\frac{{\lambda }_{2}D}{d}\Rightarrow {\lambda }_1=3.5{\lambda }_2$