Question

Coherent light that contains two wavelength, 660 nm (red) and 470nm (blue), passes through two narrow slits separated by 0.300 mm,and the interference pattern is observed on a screen 5.00 m fromthe slits. What is the distance on the screen between thefirst-order bright fringes for the two wavelengths?

Answer 1

Distance on the screen between thefirst-order bright fringes for the two wavelengths = 0.0032 m

Step-by-step explanation:

The formula for a first order bright fringe is given by:

`y_(n) = R(n \lambda /d)`

ym=R(mλ/d)

Distance between the screen and the slits, R = 5 m

Separation of the two narrow slits, d = 0.300 mm = 0.0003 m

The fringe is a first order bright fringe:

Order of the bright fringe, n = 1

Wavelength for the red light, λ =660 nm = 660*10⁻⁹ m

Wavelength for the blue light, λ =470 nm =470*10⁻⁹ m

For the first order bright fringe for red light:

`y_(r) = 5(1 * (660 * 10^(-9) /(3 * 10^(-4) )\\y_(r) = 0.011 m`

For the first order bright fringe for blue light:

`y_(b) = 5(1 * (470 * 10^(-9) /(3 * 10^(-4) )\\y_(b) = 0.0078 m`

Distance between the first order bright fringes for the two wavelengths

`y_(n) = y_(r) - y_(b) \\y_(n) = 0.011-0.0078\\y_(n) = 0.0032`

Answer 2

3.17 mm

Step-by-step explanation:

Given from the question

wavelength 1 λ₁= 660 nm = 6.6 x 10^-7 m

wavelength 2 λ₂= 470 nm = 4.7 x 10^-7 m

Distance d = 0.300 mm = 3.0 x 10^-4 m

interference L = 5.00 m

use young's slit formula :

y = k (λ L)/d . . . . . (k = order of bright fringe)

for : λ₁= 6.6 x 10^-7 m (the first-order k = 1)

y₁= 1 {(6.6 x 10^-7) (5.00)} / 3.0 x 10^-4

y₁= 11.0 x 10^-3 m = 11 mm

for : λ₂= 4.7 x 10^-7 m . . . . . . (the first-order, k = 1)

y₂= 1 {(4.7 x 10^-7 ) (5.00)} / 3.0 x 10^-4

y₂= 7.83 x 10^-3 m = 7.83 mm

so, the distance on the screen between the first-order bright fringe for each wavelength Is given by

∆y = y₁- y₂

∆y = 11mm - 7.83mm = 3.17 mm