Path difference by a slab and shifting of fringes in YDSE.

Rohit was performing a physics experiment in the physics lab.

He was performing the experiment with a bulb and an opaque paper.

He made two holes in the screen and placed the bulb behind it.

Now, he placed another opaque screen behind the existing screen to see the light from the hole, incident on the screen.

Then, he removed the second screen and found the light from the hole incident on the wall of the room.

And there was some change in the light when it was falling on the wall after passing through the holes of the first screen.

The teacher said that Young performed an experiment to explain this change of intensity of light.

Let's understand the Young double-slit experiment and find the path difference obtained.

This experiment was performed by the British physicist Thomas Young.

He used a coherent light source and an opaque screen in his experiment.

He made two slits $S_1$ and $S_2$, very close to each other, on the opaque screen.

And placed a screen at a distance $D$ from $S_1$ and $S_2$.

$S_1$ and $S_2$ behave like two coherent sources as light waves coming out of them are derived from the same original source.

And the waves emanating from $S_1$ and $S_2$ produce interference fringes on the screen at point $P$.

So, we have to find the path difference of both waves from $S_1$ and $S_2$.

We can apply the Pythagoras theorem to find the distance covered by both the waves from the slits to $P$.

We can find the path difference by finding the difference in the distance covered by both the waves.

Since the screen is very far from the source, we can change the equation.

So, the path difference is $\frac{x\times d}{D}$.

And for constructive interference, the path difference is equal to $n\lambda$.

The constructive interference will result in a bright region (fringe) when $n$ is an integer.

Similarly, for destructive interference the path difference is,

And the destructive interference will result in a dark region (fringe) when $n$ is an integer.

The distance between any two fringes (bright or dark) is called fringe width $\beta$.

And we can find the fringe width between two consecutive fringes (bright or dark).

We have discussed the path difference by a slab and the shifting of fringes in YSDE.

Revision

The Young double-slit experiment was performed by the British physicist Thomas Young.

Bright fringes are made when the constructive interference of waves occurs.

Dark fringes are made when the destructive interference of waves occurs.

The End