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Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :
- a)4 :1
- b)1 : 4
- c)1 : 2
- d)2 : 1
Correct answer is option 'D'. Can you explain this answer?
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Ratio of intensities of two light waves is given by 4 :1. The ratio of...
The correct answer is: 2 : 1
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Ratio of Intensities of Light Waves
The intensity of a light wave is directly proportional to the square of its amplitude. In other words, if the amplitude of a wave is doubled, its intensity will be four times greater. Similarly, if the amplitude is halved, the intensity will be one-fourth of the original value.
Given that the ratio of intensities of two light waves is 4:1, we can conclude that the ratio of their amplitudes will be the square root of this ratio. Let's represent the amplitudes of the waves as A1 and A2.
Mathematical Representation
The ratio of intensities (I1/I2) is given as 4:1, which can be written as:
I1/I2 = 4/1
Since intensity is proportional to the square of the amplitude, we can write it as:
(I1/I2) = (A1^2/A2^2)
Now, substitute the given ratio of intensities into the equation:
4/1 = (A1^2/A2^2)
Simplifying the Equation
To simplify the equation, we can take the square root of both sides:
√(4/1) = √(A1^2/A2^2)
2/1 = A1/A2
Therefore, the ratio of the amplitudes (A1/A2) is 2:1 or 2/1, which can be written as 2:1.
Converting the Ratio to the Given Options
The given options are:
a) 4:1
b) 1:4
c) 1:2
d) 2:1
Comparing the ratio obtained (2:1) with the given options, we can see that the correct answer is option 'd' (2:1).
Therefore, the correct ratio of the amplitudes of the waves is 2:1.
The intensity of a light wave is directly proportional to the square of its amplitude. In other words, if the amplitude of a wave is doubled, its intensity will be four times greater. Similarly, if the amplitude is halved, the intensity will be one-fourth of the original value.
Given that the ratio of intensities of two light waves is 4:1, we can conclude that the ratio of their amplitudes will be the square root of this ratio. Let's represent the amplitudes of the waves as A1 and A2.
Mathematical Representation
The ratio of intensities (I1/I2) is given as 4:1, which can be written as:
I1/I2 = 4/1
Since intensity is proportional to the square of the amplitude, we can write it as:
(I1/I2) = (A1^2/A2^2)
Now, substitute the given ratio of intensities into the equation:
4/1 = (A1^2/A2^2)
Simplifying the Equation
To simplify the equation, we can take the square root of both sides:
√(4/1) = √(A1^2/A2^2)
2/1 = A1/A2
Therefore, the ratio of the amplitudes (A1/A2) is 2:1 or 2/1, which can be written as 2:1.
Converting the Ratio to the Given Options
The given options are:
a) 4:1
b) 1:4
c) 1:2
d) 2:1
Comparing the ratio obtained (2:1) with the given options, we can see that the correct answer is option 'd' (2:1).
Therefore, the correct ratio of the amplitudes of the waves is 2:1.
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Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :a)4 :1b)1 : 4c)1 : 2d)2 : 1Correct answer is option 'D'. Can you explain this answer?
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Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :a)4 :1b)1 : 4c)1 : 2d)2 : 1Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :a)4 :1b)1 : 4c)1 : 2d)2 : 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :a)4 :1b)1 : 4c)1 : 2d)2 : 1Correct answer is option 'D'. Can you explain this answer?.
Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :a)4 :1b)1 : 4c)1 : 2d)2 : 1Correct answer is option 'D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :a)4 :1b)1 : 4c)1 : 2d)2 : 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio of intensities of two light waves is given by 4 :1. The ratio of the amplitudes of the waves is :a)4 :1b)1 : 4c)1 : 2d)2 : 1Correct answer is option 'D'. Can you explain this answer?.
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