Question

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

Answer 1

Fringe width is given by $\dfrac{D}{d}\lambda$

Position of n^th bright fringe is given by $\dfrac{nD}{d}\lambda$₁ .......(1)

Position of m^th bright fringe is given by $\dfrac{mD}{d}\lambda$₂ ........(2)

then it is given that both m^th and n^th are formed at point P

hence, equation (1)=(2)

$\implies$ $\dfrac{nD}{d}\lambda_1= \dfrac{mD}{d}\lambda_2$

$\implies$ $n{\lambda}_1=m\lambda_2$

$\implies$ $600n=400m$

$\implies$ $3n=2m$

${\implies} n= \dfrac{2}{3}m$

hence, putting m=3 we will get n=2

So, the minimum values of n and m are 2 and 3 respectively.