Question

In YDSE, the $10$th maximum of wavelength ${\lambda }_1$ is at a distance $y_1$ from its central maximum and the $5$th maximum of wavelength ${\lambda }_2$ is at a distance $y_2$ from its central maximum. The ratio $y_1/y_2$ will be :

• A. $\frac{2{\lambda }_1}{{\lambda }_2}$
• B. $\frac{2{\lambda }_2}{{\lambda }_1}$
• C. $\frac{{\lambda }_1}{2{\lambda }_2}$
• D. $\frac{{\lambda }_2}{2{\lambda }_1}$

Answer 1

The correct option is A $\frac{2{\lambda }_1}{{\lambda }_2}$

In YDSE,
$n^{th}$ maxima occurs at $\left(n\right)\frac{D\lambda }{d}$
So, ${10}^{th}$ maxima of ${\lambda }_1$ will be at:
$y_1=\left(10\right)\frac{D{\lambda }_1}{d}$$=\frac{10D{\lambda }_1}{d}$
And $5^{th}$ maxima of ${\lambda }_2$ will be at:
$y_2=\left(5\right)\frac{D{\lambda }_2}{d}$
So, $\frac{y_1}{y_2}=\frac{10D{\lambda }_1/d}{5D{\lambda }_2/d}$$=\frac{2{\lambda }_1}{{\lambda }_2}.$