Question

Monochromatic light with a wavelength of 6.4 E -7 meter passes through two narrow slits, producing an interference pattern on a screen 4.0 meters away. The first order bright band lines are 2.0 E -2 meters away from the central bright maxima. What is the distance between the slits?

1.3 E -4 m
8.0 E -6 m
3.2 E -9 m
7.8 E3 m

Answer 1

1.3 E -4 m

Step-by-step explanation:

I took the test :)

Answer 2

The distance between the slits is given by 1.3 ×
`10^(-4)` m

Given:

`\lambda = 6.4 * 10^(-7) m`

D = 4 m

y =
`2 * 10^(-2) m`

m = 1

To find:

distance between slits, d = ?

Formula used:

y =
`(m * \lambda * D)/(d)`

y = distance of first bright band from central maxima

D = distance between screen and source

d = distance between slits

`\lambda` = wavelength

Solution:

distance of first bright band from central maxima is given by,

y =
`(m * \lambda * D)/(d)`

y = distance of first bright band from central maxima

D = distance between screen and source

d = distance between slits

`\lambda` = wavelength

Thus,

d =
`(m * \lambda * D)/(y)`

d =
`(1 * 6.4 * 10^(-7) * 4 )/(2 * 10^(-2) )`

d = 1.28 ×
`10^(-4)`

d = 1.3 ×
`10^(-4)` m

The distance between the slits is given by 1.3 ×
`10^(-4)` m