In a YDSE,bichromatic light of wavelengths la | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The condition for the $n^{th}$ minima for wavelength $\lambda$ is given by $y_n = (2n-1) \frac{D\lambda}{2d}$.For two wavelengths to have overlapp

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(D) The condition for the $n^{th}$ minima for wavelength $\lambda$ is given by $y_n = (2n-1) \frac{D\lambda}{2d}$.For two wavelengths to have overlapping dark fringes,their minima must coincide: $(2n-1) \frac{D\lambda_1}{2d} = (2m-1) \frac{D\lambda_2}{2d}$.This simplifies to $(2n-1) \lambda_1 = (2m-1) \lambda_2$.Substituting the values: $(2n-1) 400 = (2m-1) 560$.$\frac{2n-1}{2m-1} = \frac{560}{400} = \frac{7}{5}$.Thus,the first overlap occurs at $2n-1 = 7$ (i.e.,$n=4$) and $2m-1 = 5$ (i.e.,$m=3$).The position of this first overlap is $y_1 = 7 	imes \frac{1 	imes 400 	imes 10^{-6}}{2 	imes 0.1 	imes 10^{-3}} = 14 	imes 10^{-3}\, m = 14\, mm$.The next overlap occurs at the next odd multiple ratio,which is $\frac{21}{15}$ (where $2n-1=21$ and $2m-1=15$).The position of this second overlap is $y_2 = 21 	imes \frac{1 	imes 400 	imes 10^{-6}}{2 	imes 0.1 	imes 10^{-3}} = 42\, mm$.The distance between two successive regions of complete darkness is $y_2 - y_1 = 42\, mm - 14\, mm = 28\, mm$.

Similar Questions

In Young's double slit experiment,if the distance between the two slits is halved,then the fringe width will become

The Young's double slit experiment is performed in succession using blue light of wavelength $4360 \, \mathring{A}$ and green light of wavelength $5460 \, \mathring{A}$. If the distance of the fourth maximum from the central maximum is $x$,then:

The path difference between two identical light waves at a point $Q$ on the screen is $3 \mu m$. If the wavelength of the waves is $5000 \text{ Å}$,then at point $Q$ there is:

If yellow light emitted by a sodium lamp in Young's double-slit experiment is replaced by monochromatic blue light of the same intensity,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module