Ayoung's interference experiment is performed with blue-green argon laser light. the separation between the slits is 0.500 mm, and the screen is located 3.30 m from the slits. the first bright fringe is located 3.40 mm from the center of the interference pattern. what is the wavelengtl of the argon laser light?

The wavelength of the argon laser light is 515 nm

Explanation:

For bright spot,

The relation between the distance of the slits and the angle through which it is passed is:

dsinθ=nλ

where,

n can be any integer

d is the distance between the two slits

λ is the wavelength of light.

Since for the first bright fringe, n=1

The experiment sceneerio can be drawn with the help of an image shown below.

So,

Using Pythagoras theorem for ΔABC

AB² + BC² = AC²

Thus,

AC² = (3300)² + (3.40)²

AC = 3300.0018 mm

sinθ = 3.40/3300.0018 = 0.001030

Applying the values in the formula as:

0.5 mm×0.001030=(1)λ

So,

The wavelength = 0.000515 mm

Also, 1 mm = 10⁶ nm

So, wavelength = 515 nm

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.