Question

In a Young's double slit experiment, $m$ th order and $n$ th order of bright fringes are formed at point $P$ on a distant screen, if monochromatic source of wavelength $400\, nm$ and $600\, nm$ are used respectively. The minimum value of $m$ and $n$ are respectively,

• A. 4,6
• B. 3,2
• C. 2,3
• D. 4,2

Answer 1

Answer: (B)

Let $m^{\text {th }}$ bright fringe of wavelength $\lambda_{m}$ and $n^{\text {th }}$ bright fringe of wave length $\lambda_{n}$ formed at a distance $x_{n}$ from central maxima at same point $P$,
i.e., they coincide, therefore, $x_{m}=x_{n}$.
$\frac{m \lambda_{m} D}{d}=\frac{n \lambda_{n} D}{d}$
$ \Rightarrow \frac{m}{n}=\frac{\lambda_{n}}{\lambda_{m}}$
Putting the given values, we get
$=\frac{600 \times 10^{-9}}{400 \times 10^{-9}}$
$\left[\right.$ Given, $\left.\lambda_{m}=400 \times 10^{-9} m , \lambda_{n}=600 \times 10^{-9} m \right]$
$\therefore \frac{m}{n}=\frac{3}{2}$
So, least integral values of $m$ and $n$ satisfying above requirement are $m=3$ and $n=2$.