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

Answer:

Slit separation, $d=3.25\times 10^{-4}\ m$

Explanation:

It is given that,

Wavelength of laser light, $\lambda=650\ nm=650\times 10^{-9}\ m$

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, $sin\theta=tan\theta=\dfrac{y}{L}$

$d(\dfrac{y}{L})=n\lambda$

$d=\dfrac{n\lambda L}{y}$

$d=\dfrac{10\times 650\times 10^{-9}\times 1.5}{0.03}$

d = 0.000325 m

or

$d=3.25\times 10^{-4}\ m$

So, the separation between the slits is $3.25\times 10^{-4}\ m$. Hence, this is the required solution.