In a certain region of the screen, number of fringes formed is observed to be 8 in Young's double slit experiment when light of wavelength 6600 A ˚ is used. If the light of wavelength 4400 A ˚ is

Question

In a certain region of the screen, number of fringes formed is observed to be 8 in Young's double slit experiment when light of wavelength 6600 A ˚ is used. If the light of wavelength 4400 A ˚ is used, the number of fringes observed in the same region of the screen will be

TestHub · Accepted Answer

Let the width of the region on the screen be $y$ .

The fringe width is given by $β = \frac{λ D}{d}$

The number of fringes $n$ in the region $y$ is $n = \frac{y}{β} = \frac{y d}{λ D}$

For a fixed region, $n \propto \frac{1}{λ}$

$n_{1} λ_{1} = n_{2} λ_{2}$

Given $n_{1} = 8$ , $λ_{1} = 6600 \overset{˚}{A}$ , and $λ_{2} = 4400 \overset{˚}{A}$

$8 \times 6600 = n_{2} \times 4400$

$n_{2} = \frac{8 \times 6600}{4400} = 12$

Answer: $12$

Physics - Wave Optics Question with Solution | TestHub

Options:

Doubts & Discussion