# What does interference really mean? Path length difference.

At a particular point on a screen illuminated by two slits, the path length from that point to the bottom slit is greater than to the top slit. Which of the following statements are true about the path-length difference between the two waves arriving at the screen?

(True/False Problem)

1. a bright line will appear if the difference in path lengths is three wavelengths.

2. a bright line will appear if the difference in path lengths is 3/2 wavelengths.

3. a dark line will appear if the difference in path lengths is half a wavelength.

4. a bright line will appear if the difference in path lengths is 1/4 of a wavelength.

5. a dark line will appear if the difference in path lengths is two wavelengths.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

When two waves superpose on each other at a point, the phenomena of interference takes place. If at the given point the crests (or troughs) of the two waves coincide, the amplitude of the resultant wave is the sum of the amplitudes of the individual waves and constructive interference is said to take place at the point. A bright band is formed at that point. On the other hand if the crest of one wave coincides with the trough of the other at a point, the resultant wave has an amplitude equal to the difference of two individual amplitudes and destructive interference is said to take place. a dark band appears at that point.

In case of double slit interference, the waves from the two slits are coherent (i.e. both have zero phase difference or constant phase difference at the slits at all times) and monochromatic (i.e of only one frequency or color). In that case, if the distances travelled by the waves from two slits are different by an integral multiple of their wave length, the crests of the two will coincide and constructive interference will take place.

On the other hand if the path difference is an odd multiple of half a wave length, crest of one will coincide with the trough of the other resulting in destructive interference.

Now let us examine the given options:

1: True because path difference is an integral multiple of a wave length resulting in constructive interference.

2: False becuase path difference is an odd multiple of half wavelength which is the condition for destructive interference.

3: True because half a wave length path difference implies destructive interference.

4: False as condition for constructive interference not satisfied.

5: False as the given condition is for constructive inteference.

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