Question

In YDSE, if bichromatic light having wavelength ${\lambda }_1$ and ${\lambda }_2$ is used, then the maxima due to both lights will overlap at a distance of ...... from the central maxima. Take separation between slits as $d$ and distance between screen and slits as $D$. Most appropriate option.. for the blank space is :

• A. $\left(\frac{{\lambda }_1+{\lambda }_2}{2D}\right)d$
• B. $\left(\frac{{\lambda }_1-{\lambda }_2}{2D}\right)\times 2d$
• C. LCM of $\frac{{\lambda }_{1}D}{d}$ and $\frac{{\lambda }_{2}D}{d}$
• D. HCF of $\frac{{\lambda }_{1}D}{d}$ and $\frac{{\lambda }_{2}D}{d}$

Answer 1

The correct option is C LCM of $\frac{{\lambda }_{1}D}{d}$ and $\frac{{\lambda }_{2}D}{d}$

Let $n_1$ bright order of wavelenth ${\lambda }_1$ coincides with $n_2$ bright order of wavelenth ${\lambda }_2$

Its distance from central maximum $y=\frac{n_1{\lambda }_{1}D}{d}=$$\frac{n_2{\lambda }_{2}D}{d}$ which gives LCM $of\frac{{\lambda }_{1}D}{d}and\frac{{\lambda }_{2}D}{d}$