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When two coherent monochromatic light beams of intensities I and 4I are superimposed, the ratio between maximum and minimum intensities in the resultant beam is
- a)9:1
- b)1:9
- c)4:1
- d)1:4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
When two coherent monochromatic light beams of intensities I and 4I ar...
Calculation of Intensity
Intensity of a monochromatic wave is directly proportional to the square of its amplitude. Therefore, the intensity ratio of the two given waves can be written as:
I1/I2 = (A1/A2)^2
where A1 and A2 are the amplitudes of the two waves.
Given that I1/I2 = 1/4, we can write:
A1/A2 = 1/2
Superposition of Waves
When two waves superimpose, the resulting wave is given by the principle of superposition, which states that the displacement of the medium at any point is the algebraic sum of the displacements due to each wave.
If the two waves have the same amplitude and frequency, the resulting wave is a wave of the same frequency with an amplitude that can vary from zero to twice the amplitude of the individual waves, depending on the phase relationship between the waves.
In this case, however, the two waves have different intensities. Therefore, the resulting wave will have an intensity that varies from the sum of the individual intensities to the difference between the two intensities, depending on the phase relationship between the waves.
Ratio of Maximum and Minimum Intensities
The maximum intensity of the resulting wave occurs when the two waves are in phase, i.e., the crests and troughs of the waves coincide. In this case, the intensity of the resulting wave is the sum of the individual intensities:
I_max = I1 + I2 = I + 4I = 5I
The minimum intensity of the resulting wave occurs when the two waves are out of phase, i.e., the crest of one wave coincides with the trough of the other wave. In this case, the intensity of the resulting wave is the difference between the individual intensities:
I_min = I2 - I1 = 3I
Therefore, the ratio of maximum to minimum intensities is:
I_max/I_min = 5I/3I = 5/3 = 1.67
However, the question asks for the ratio of minimum to maximum intensities, which is the reciprocal of the above ratio:
I_min/I_max = 3/5 = 0.6
But none of the given options match this value.
Therefore, the correct answer is none of the above.
(Note: There may be an error in the question or the options provided.)
Intensity of a monochromatic wave is directly proportional to the square of its amplitude. Therefore, the intensity ratio of the two given waves can be written as:
I1/I2 = (A1/A2)^2
where A1 and A2 are the amplitudes of the two waves.
Given that I1/I2 = 1/4, we can write:
A1/A2 = 1/2
Superposition of Waves
When two waves superimpose, the resulting wave is given by the principle of superposition, which states that the displacement of the medium at any point is the algebraic sum of the displacements due to each wave.
If the two waves have the same amplitude and frequency, the resulting wave is a wave of the same frequency with an amplitude that can vary from zero to twice the amplitude of the individual waves, depending on the phase relationship between the waves.
In this case, however, the two waves have different intensities. Therefore, the resulting wave will have an intensity that varies from the sum of the individual intensities to the difference between the two intensities, depending on the phase relationship between the waves.
Ratio of Maximum and Minimum Intensities
The maximum intensity of the resulting wave occurs when the two waves are in phase, i.e., the crests and troughs of the waves coincide. In this case, the intensity of the resulting wave is the sum of the individual intensities:
I_max = I1 + I2 = I + 4I = 5I
The minimum intensity of the resulting wave occurs when the two waves are out of phase, i.e., the crest of one wave coincides with the trough of the other wave. In this case, the intensity of the resulting wave is the difference between the individual intensities:
I_min = I2 - I1 = 3I
Therefore, the ratio of maximum to minimum intensities is:
I_max/I_min = 5I/3I = 5/3 = 1.67
However, the question asks for the ratio of minimum to maximum intensities, which is the reciprocal of the above ratio:
I_min/I_max = 3/5 = 0.6
But none of the given options match this value.
Therefore, the correct answer is none of the above.
(Note: There may be an error in the question or the options provided.)
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When two coherent monochromatic light beams of intensities I and 4I are superimposed, the ratio between maximum and minimum intensities in the resultant beam isa) 9:1 b) 1:9 c) 4:1 d) 1:4 Correct answer is option 'A'. Can you explain this answer?
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