Question

Two wavelengths of light ${\lambda }_1$ and ${\lambda }_2$ are sent through Young's double-slit apparatus simultaneously. If the third-order bright fringe coincides with the fourth-order bright fringe, then

• A. $\frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{3}$
• B. $\frac{{\lambda }_1}{{\lambda }_2}=\frac{3}{4}$
• C. $\frac{{\lambda }_1}{{\lambda }_2}=\frac{5}{4}$
• D. $\frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{5}$

Answer 1

The correct option is A $\frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{3}$

${\beta }_1={\lambda }_1\frac{D}{d}$

position for third order bright fringe, $y_1=3{\beta }_1=3{\lambda }_1\frac{D}{d}$

${\beta }_2={\lambda }_2\frac{D}{d}$

position for third order bright fringe, $y_2=4{\beta }_2=3{\lambda }_2\frac{D}{d}$

Since $y_1=y_2$

$3{\lambda }_1\frac{D}{d}=4{\lambda }_2\frac{D}{d}$

=> $\frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{3}$

Answer. A) $\frac{4}{3}$