Question

Two beams of light will not give rise to an interference pattern, if

• A. They are coherent
• B. They have the same wavelength
• C. They are linearly polarized perpendicular to each other
• D. They are monochromatic

Answer 1

The correct option is C

They are linearly polarized perpendicular to each other

Explanation for correct option:

Option (C):

1. An important consequence of the principle of superposition is that when two beams of light intersect, the propagation of each beam is completely unaffected by the presence of the other.
2. However, in the region of crossing both the beams act simultaneously and we expect a change in intensity.
3. A case of utmost importance occurs when monochromatic waves of light from two sources proceed almost in the same direction and superpose at a point either in the same or in the opposite phase.
4. Then the intensity of light at that point will be maximum or minimum according to whether the waves meet the point in the same or in the opposite phase.
5. This phenomenon is known as the interference of light.
6. Hence, for interference to occur we require two light sources that have the same frequency and phase difference.
7. This can be achieved by allowing light from a point source to pass through two equal slits.
8. Therefore, for interference to occur the two light sources must both be perpendicular to the plane joining the slit and the screen.
9. They cannot be polarized perpendicular to each other.
10. Perpendicular polarization occurs when the electric component of wave vectors travels in a perpendicular direction to that surface on which the interaction occurs, considering the direction of the wave axis.
11. It is widely known as an s-polarized wave and occurs along longitudinal.
12. Two waves, linearly polarized with perpendicular polarizations, if derived from perpendicular components of unpolarized light and subsequently brought into the same plane, cannot interfere.
13. Two waves, linearly polarized with perpendicular polarizations, if derived from the same linearly polarized wave and subsequently brought into the same plane, can interfere.

Explanation for incorrect options:

Option (A):

1. From the above explanation, we can see that for interference to occur we require two coherent sources of light.
2. Coherent sources are when two light sources have the same frequency and phase difference.
3. Therefore, two beams of light will give rise to an interference pattern, if they are coherent.

Option (B):

1. From the above explanation, we can see that for interference to occur we require two coherent sources of light.
2. Coherent sources are when two light sources have the same frequency and phase difference.
3. We know that wavelength is inversely proportional to frequency.
4. Therefore, two beams of light will give rise to an interference pattern, if they have the same wavelength.

Option (D):

1. From the above explanation, we can see that for interference to occur we require two coherent sources of light.
2. Coherent sources are when two light sources have the same frequency and phase difference.
3. Monochromatic light has the same frequency and wavelength throughout.
4. Therefore, two beams of light will give rise to an interference pattern, if they are monochromatic.

Hence, the correct answer is option (C).