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In the Young's double slit experiment, the interference pattern is found to have an intensity ratio between the bright and dark fringes as 9. This implies that
- a)the intensities at the screen due to the two slits are 5 units and 4 units, respectively
- b)the intensities at the screen due to the two slits are 4 units and 1 unit, respectively
- c)the amplitude ratio is 3
- d)the amplitude ratio is 2
Correct answer is option 'B,C'. Can you explain this answer?
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In the Young's double slit experiment, the interference pattern is fo...
Explanation:
The intensity ratio between the bright and dark fringes in Young's double slit experiment can be determined using the principle of interference.
Interference Principle:
When two coherent light waves from two different sources interfere with each other, the resultant intensity at a point on the screen is given by the superposition of the two waves. If the two waves have the same amplitude and phase, they will constructively interfere and produce a bright fringe. If they have opposite phases, they will destructively interfere and produce a dark fringe.
Intensity Ratio:
The intensity at a point on the screen due to interference is proportional to the square of the amplitude of the resultant wave. Let's assume the amplitude of the wave from the first slit is A₁ and the amplitude of the wave from the second slit is A₂.
The intensity at a bright fringe is given by:
I(bright) = (A₁ + A₂)²
The intensity at a dark fringe is given by:
I(dark) = (A₁ - A₂)²
The intensity ratio between the bright and dark fringes is given by:
I(bright) / I(dark) = (A₁ + A₂)² / (A₁ - A₂)²
Simplifying this expression:
I(bright) / I(dark) = (A₁ + A₂) / (A₁ - A₂) * (A₁ + A₂) / (A₁ - A₂)
Since we are given that the intensity ratio is 9, we can write:
9 = (A₁ + A₂) / (A₁ - A₂) * (A₁ + A₂) / (A₁ - A₂)
Squaring both sides:
81 = [(A₁ + A₂) / (A₁ - A₂)]²
Taking the square root of both sides:
√81 = (A₁ + A₂) / (A₁ - A₂)
Simplifying:
9 = (A₁ + A₂) / (A₁ - A₂)
Now, let's consider the options given:
a) The intensities at the screen due to the two slits are 5 units and 4 units, respectively.
If we plug in these values into the equation, we get:
9 = (5 + 4) / (5 - 4) = 9/1 = 9
So, this option satisfies the given intensity ratio.
b) The intensities at the screen due to the two slits are 4 units and 1 unit, respectively.
If we plug in these values into the equation, we get:
9 = (4 + 1) / (4 - 1) = 5/3
So, this option does not satisfy the given intensity ratio.
c) The amplitude ratio is 3.
If we plug in this value into the equation, we get:
9 = (3 + 1) / (3 - 1) = 4/2 = 2
So, this option does not satisfy the given intensity ratio.
d) The amplitude ratio is 2.
If we plug in this value into the equation, we get:
9 = (2 + 1) / (2 - 1) = 3/1 = 3
So, this option satisfies the given intensity ratio.
Therefore,
The intensity ratio between the bright and dark fringes in Young's double slit experiment can be determined using the principle of interference.
Interference Principle:
When two coherent light waves from two different sources interfere with each other, the resultant intensity at a point on the screen is given by the superposition of the two waves. If the two waves have the same amplitude and phase, they will constructively interfere and produce a bright fringe. If they have opposite phases, they will destructively interfere and produce a dark fringe.
Intensity Ratio:
The intensity at a point on the screen due to interference is proportional to the square of the amplitude of the resultant wave. Let's assume the amplitude of the wave from the first slit is A₁ and the amplitude of the wave from the second slit is A₂.
The intensity at a bright fringe is given by:
I(bright) = (A₁ + A₂)²
The intensity at a dark fringe is given by:
I(dark) = (A₁ - A₂)²
The intensity ratio between the bright and dark fringes is given by:
I(bright) / I(dark) = (A₁ + A₂)² / (A₁ - A₂)²
Simplifying this expression:
I(bright) / I(dark) = (A₁ + A₂) / (A₁ - A₂) * (A₁ + A₂) / (A₁ - A₂)
Since we are given that the intensity ratio is 9, we can write:
9 = (A₁ + A₂) / (A₁ - A₂) * (A₁ + A₂) / (A₁ - A₂)
Squaring both sides:
81 = [(A₁ + A₂) / (A₁ - A₂)]²
Taking the square root of both sides:
√81 = (A₁ + A₂) / (A₁ - A₂)
Simplifying:
9 = (A₁ + A₂) / (A₁ - A₂)
Now, let's consider the options given:
a) The intensities at the screen due to the two slits are 5 units and 4 units, respectively.
If we plug in these values into the equation, we get:
9 = (5 + 4) / (5 - 4) = 9/1 = 9
So, this option satisfies the given intensity ratio.
b) The intensities at the screen due to the two slits are 4 units and 1 unit, respectively.
If we plug in these values into the equation, we get:
9 = (4 + 1) / (4 - 1) = 5/3
So, this option does not satisfy the given intensity ratio.
c) The amplitude ratio is 3.
If we plug in this value into the equation, we get:
9 = (3 + 1) / (3 - 1) = 4/2 = 2
So, this option does not satisfy the given intensity ratio.
d) The amplitude ratio is 2.
If we plug in this value into the equation, we get:
9 = (2 + 1) / (2 - 1) = 3/1 = 3
So, this option satisfies the given intensity ratio.
Therefore,
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In the Young's double slit experiment, the interference pattern is fo...
Ratio of maximum to minimum intensity of the interference pattern
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In the Young's double slit experiment, the interference pattern is found to have an intensity ratio between the bright and dark fringes as 9. This implies thata)the intensities at the screen due to the two slits are 5 units and 4 units, respectivelyb)the intensities at the screen due to the two slits are 4 units and 1 unit, respectivelyc)the amplitude ratio is 3d)the amplitude ratio is 2Correct answer is option 'B,C'. Can you explain this answer?
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