Question

3. A laser with a wavelength of 650 nm passes through a double slit. A pattern is observed on a wall that is 1.5 meters away from the slits. The spacing between 10 bright fringes is measured to be 3 cm. Calculate the separation between the slits. Show your work.

Answer 1

Slit separation,
`d=3.25* 10^(-4)\ m`

Step-by-step explanation:

It is given that,

Wavelength of laser light,
`\lambda=650\ nm=650* 10^(-9)\ m`

Distance between pattern and the wall, L = 1.5 m

The spacing between 10 bright fringes is, y = 3 cm = 0.03 m

We need to find the separation between the slits. According to the equation of diffraction law :

`d\ sin\theta=n\lambda`

Where

d is the separation between the slits

For smaller angles,
`sin\theta=tan\theta=(y)/(L)`

`d((y)/(L))=n\lambda`

`d=(n\lambda L)/(y)`

`d=(10* 650* 10^(-9)* 1.5)/(0.03)`

d = 0.000325 m

or

`d=3.25* 10^(-4)\ m`

So, the separation between the slits is
`3.25* 10^(-4)\ m`. Hence, this is the required solution.