Question

35.15 .. Coherent light with wavelength 600 nm passes through two very narrow slits and the interference pattern is observed on a screen 3.00 m from the slits. The first-order bright fringe is at 4.84 mm from the center of the central bright fringe. For what wavelength of light will the first-order dark fringe be observed at this same point on the screen

Answer 1

`1.199\ \mu\text{m}`

Step-by-step explanation:

`\lambda` = Wavelength = 600 nm

D = Distance of the light source from screen = 3 m

y = Distance of first order bright fringe from center = 4.84 mm

d = Distance between slits

m = Order = 1

We have the relation

`y=(D\lambda)/(d)\\\Rightarrow d=(D\lambda)/(y)\\\Rightarrow d=(3* 600* 10^(-9))/(4.84* 10^(-3))\\\Rightarrow d=0.0003719\ \text{m}`

From the question we have

`y=((1)/(2)3\lambda)/(d)\\\Rightarrow \lambda=(2)/(3)yd\\\Rightarrow \lambda=(2)/(3)* 4.84* 10^(-3)* 0.0003719\\\Rightarrow \lambda=0.000001199\ \text{m}=1.199\ \mu\text{m}`

The required wavelength of light is
`1.199\ \mu\text{m}`.