Question

In a YDSE, if the incident light consists of two wavelengths ${\lambda }_1$ and ${\lambda }_2$, the slit separation is $d$, and the distance between the slit and the screen is $D$, the maxima due to each wavelength will coincide at a distance from the central maxima, given by

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

Answer 1

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