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Two coherent light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are
- a)5 / and /
- b)5 / and 3/
- c)9 / and /
- d)9 / and 3/
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two coherent light beams of intensities I and 4I are superposed. The m...
I1=I and I2=4I therefore; I max=(√I1 + √I2)^2 I max= (3√I)^2 I max=9I and for I min=(√I1-√I2)^2 I min=(√1-(√4I)^2 I min=1.. so the final answer is 9I and I so option c is correct answer.
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Two coherent light beams of intensities I and 4I are superposed. The m...
Understanding Coherent Light Beams
When two coherent light beams with different intensities interfere, we can calculate the maximum and minimum intensities of the resulting beam through the principles of interference.
Given Intensities
- Let the intensities of the two beams be:
- I1 = I (first beam)
- I2 = 4I (second beam)
Maximum Intensity Calculation
- The maximum intensity (I_max) occurs when the beams are in phase. The formula for calculating maximum intensity is:
I_max = I1 + I2 + 2√(I1 * I2)
- Applying the values:
I_max = I + 4I + 2√(I * 4I)
I_max = 5I + 2√(4I^2) = 5I + 4I = 9I
Minimum Intensity Calculation
- The minimum intensity (I_min) occurs when the beams are out of phase. The formula for minimum intensity is:
I_min = I1 + I2 - 2√(I1 * I2)
- Applying the values:
I_min = I + 4I - 2√(4I^2)
I_min = 5I - 4I = I
Final Result
- Thus, the maximum and minimum intensities of the resulting beam are:
- Maximum Intensity = 9I
- Minimum Intensity = I
The correct option for the maximum and minimum intensities in the resulting beam is C) 9I and I. This reflects the constructive and destructive interference of the two coherent light beams.
When two coherent light beams with different intensities interfere, we can calculate the maximum and minimum intensities of the resulting beam through the principles of interference.
Given Intensities
- Let the intensities of the two beams be:
- I1 = I (first beam)
- I2 = 4I (second beam)
Maximum Intensity Calculation
- The maximum intensity (I_max) occurs when the beams are in phase. The formula for calculating maximum intensity is:
I_max = I1 + I2 + 2√(I1 * I2)
- Applying the values:
I_max = I + 4I + 2√(I * 4I)
I_max = 5I + 2√(4I^2) = 5I + 4I = 9I
Minimum Intensity Calculation
- The minimum intensity (I_min) occurs when the beams are out of phase. The formula for minimum intensity is:
I_min = I1 + I2 - 2√(I1 * I2)
- Applying the values:
I_min = I + 4I - 2√(4I^2)
I_min = 5I - 4I = I
Final Result
- Thus, the maximum and minimum intensities of the resulting beam are:
- Maximum Intensity = 9I
- Minimum Intensity = I
The correct option for the maximum and minimum intensities in the resulting beam is C) 9I and I. This reflects the constructive and destructive interference of the two coherent light beams.
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Two coherent light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam area)5 / and /b)5 / and 3/c)9 / and /d)9 / and 3/Correct answer is option 'C'. Can you explain this answer?
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