Question

Light with wavelength λ is incident on a double slit with spacing d. A pattern is observed on a screen which is far from the slits (compared to the separation between the slits).

a.) Explain whether each of the following is correct or not.

1.) The pattern looks like a wave with bright fringes separated by a distance λ.

2.) The pattern looks like a wave with bright fringes separated by distance d.

3.) The pattern looks like a wave with the locations of the bright fringes determined by the wavelength only.

4.) The pattern looks like a wave with the locations of the bright fringes determined by the slit separation only.

b.) The wave length is doubled to 2λ and the split spacing is also doubled to 2d. Which of the following is true? Explain your answer.

1.) The separation between the fringes is a quarter of what it was before.

2.) The separation between the fringes is a half of what it was before.

3.) The separation between the fringes is the same as before.

4.) The separation between the fringes doubles.

5.) The separation between the fringes increases by four times.

Answer 1

From the above diagram we can say that position of bright fringes is given as:

So, position First bright fringe is:

Position of second bright fringe is :

So, sapration between fringes is:

So we can sa that pattern look like a wave with bright fringes saparated by a distance ​​​​​​

So, option (1) and (2) both are not correct

Similarly,

We can also say that distance between two bright fringes is depend on both wavelength and distance between slits

So, (3) and (4) will also be incorrect

Part(b)

We know that fringes sapration are given as:

When the wavelength and slits sapartion is doubled then:

We can say that the sapration will remain unchanged so, option (3) is correct