Question

A pair of narrow slits that are 1.8 mm apart is illuminated by a monochromatic coherent light source. A fringe pattern is observed on a screen 4.8 m from the slits. If there are 5.0 bright fringes/cm on the screen, what is the wavelength of the monochromatic light?

Answer 1

The wavelength of the monochromatic light is
`7.5*10^(-7)\ m`

Step-by-step explanation:

Given that,

Distance between the slits d = 1.8 mm

Distance of fringe from the slits D =4.8 m

Number of fringe m =1

Distance between the fringes = 1 cm

We need to calculate the wavelength of monochromatic light

Using formula of young's double slits

`\lambda=(Yd)/(mD)`

Where, d = Distance between the slits

D = Distance of fringe from the slits

m = Number of fringe

y = Distance between the fringes

Put the value in to the formula

`\lambda=(1*10^(-2)*1.8*10^(-3))/(5*4.8)`

`\lambda =7.5*10^(-7)\ m`

Hence, The wavelength of the monochromatic light is
`7.5*10^(-7)\ m`

Answer 2

750 mm

Step-by-step explanation:

Given:

d = 1.8 mm

R = 4.8 m

m = 5

y = 1

Using the equation

y = (mLR)/d ,

where,

m gives a distance 'y' to that particular slit image.

R = distance from the double slits to the screen

d = double slit separation distance.

L = wavelength of the light.

substituting the values in the given equation

we get

L =
`(1* 1.8* 10^(-3))/(5* 4.8)`

or

L = 750 mm