Question

A ray of light contains two colors: red with wavelength of 660 nm and blue with wavelength 470 nm. The ray passes through two narrow slits separated by 0.30 mm and the interference pattern is observed on a screen 5.0 m from the slits. What is the distance on the screen between the first-order bright fringes for each wavelength?

Answer 1

Answer:

The distance on the screen between the first-order bright fringes  for each wavelength is 3.17 mm.

Explanation:

Given that,

Wavelength of red = 660 nm

Wavelength of blue = 470 nm

Separated d= 0.30 mm

Distance between screen and slits D= 5.0 m

We need to calculate the distance for red wavelength

Using formula for distance

$y=\dfrac{\lambda D}{d}$

Where, D = distance between screen and slits

d = separation of slits

Put the value into the formula

$y=\dfrac{660\times10^{-9}\times5.0}{0.30\times10^{-3}}$

$y=11\ mm$

For blue wavelength,

Put the value into the formula again

$y'=\dfrac{470\times10^{-9}\times5.0}{0.30\times10^{-3}}$

$y'=7.83\ mm$

We need to calculate the distance on the screen between the first-order bright fringes for each wavelength

Using formula for distance

$\Delta y=y-y'$

$\Delta y=11-7.83$

$\Delta y=3.17\ mm$

Hence, The distance on the screen between the first-order bright fringes  for each wavelength is 3.17 mm.