Question

Light from a source emitting two wavelengths ${\lambda }_1$ and ${\lambda }_2$ is allowed to fall on Young's double-slit apparatus after filtering one of the wavelengths. The position of interference maxima is noted. When the filter is removed both the wavelengths are incident and it is found that maximum intensity is produced where the the fourth maxima occurred previously. If other wavelength is filtered, at the same location the third maxima is found. What is the ratio of wavelengths?

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{3}{4}$
• D. $\frac{4}{3}$

Answer 1

The correct option is C $\frac{3}{4}$

The height above central maxima is same in both the cases (i.e. position of maxima in both cases is the same)

Therefore,

$n_1{\lambda }_1=n_2{\lambda }_2$

$4\times {\lambda }_1=3\times {\lambda }_2$

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