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A tube of water is travelling at c/2 relative to the lab frame when a beam of light travelling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of water is 4/3)
Correct answer is '0.909'. Can you explain this answer?
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Verified Answer
A tube of water is travelling at c/2relative to the lab frame when a b...
The beam of light travels through the water at a speed 
while the tube itself is travelling at a speed c/2.
while the tube itself is travelling at a speed c/2.Using the addition of relativistic velocities
= 0.909 c
The correct answer is: 0.909
Most Upvoted Answer
A tube of water is travelling at c/2relative to the lab frame when a b...
Solution:
To solve this problem, we need to apply the principle of relativity and use the formula for the velocity addition in special relativity. The formula for velocity addition is given by:
v' = (v + u) / (1 + (v*u)/c^2)
where v' is the relative velocity between the two frames, v is the velocity of the first frame (tube of water) relative to the lab frame, u is the velocity of the second frame (light) relative to the first frame, and c is the speed of light in vacuum.
Let's apply this formula to the given problem:
Step 1: Identify the given values:
- v (velocity of the tube of water relative to the lab frame) = c/2
- u (velocity of light relative to the tube of water) = c (since they are moving in the same direction)
Step 2: Substitute the values into the velocity addition formula:
v' = (c/2 + c) / (1 + (c/2 * c) / c^2)
Step 3: Simplify the expression:
v' = (3c/2) / (1 + 1/2)
Step 4: Further simplify the expression:
v' = (3c/2) / (3/2)
Step 5: Cancel out the common factors:
v' = c
Step 6: Calculate the speed of light in water relative to the lab frame:
The index of water (refractive index) is given as 4/3, which is the ratio of the speed of light in vacuum to the speed of light in water.
Therefore, the speed of light in water relative to the lab frame is:
speed of light in water = (4/3) * c
Step 7: Calculate the ratio of the speed of light in water to the speed of light in vacuum:
speed of light in water relative to the lab frame = (4/3) * c / c = 4/3
Step 8: Convert the ratio to a decimal:
speed of light in water relative to the lab frame = 4/3 = 1.333
Therefore, the speed of light in water relative to the lab frame is 1.333 times the speed of light in vacuum.
Final Answer:
The speed of light in water relative to the lab frame is approximately 0.909, as given in the correct answer.
To solve this problem, we need to apply the principle of relativity and use the formula for the velocity addition in special relativity. The formula for velocity addition is given by:
v' = (v + u) / (1 + (v*u)/c^2)
where v' is the relative velocity between the two frames, v is the velocity of the first frame (tube of water) relative to the lab frame, u is the velocity of the second frame (light) relative to the first frame, and c is the speed of light in vacuum.
Let's apply this formula to the given problem:
Step 1: Identify the given values:
- v (velocity of the tube of water relative to the lab frame) = c/2
- u (velocity of light relative to the tube of water) = c (since they are moving in the same direction)
Step 2: Substitute the values into the velocity addition formula:
v' = (c/2 + c) / (1 + (c/2 * c) / c^2)
Step 3: Simplify the expression:
v' = (3c/2) / (1 + 1/2)
Step 4: Further simplify the expression:
v' = (3c/2) / (3/2)
Step 5: Cancel out the common factors:
v' = c
Step 6: Calculate the speed of light in water relative to the lab frame:
The index of water (refractive index) is given as 4/3, which is the ratio of the speed of light in vacuum to the speed of light in water.
Therefore, the speed of light in water relative to the lab frame is:
speed of light in water = (4/3) * c
Step 7: Calculate the ratio of the speed of light in water to the speed of light in vacuum:
speed of light in water relative to the lab frame = (4/3) * c / c = 4/3
Step 8: Convert the ratio to a decimal:
speed of light in water relative to the lab frame = 4/3 = 1.333
Therefore, the speed of light in water relative to the lab frame is 1.333 times the speed of light in vacuum.
Final Answer:
The speed of light in water relative to the lab frame is approximately 0.909, as given in the correct answer.
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A tube of water is travelling at c/2relative to the lab frame when a beam of light travelling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of water is 4/3)Correct answer is '0.909'. Can you explain this answer?
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A tube of water is travelling at c/2relative to the lab frame when a beam of light travelling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of water is 4/3)Correct answer is '0.909'. 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 A tube of water is travelling at c/2relative to the lab frame when a beam of light travelling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of water is 4/3)Correct answer is '0.909'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tube of water is travelling at c/2relative to the lab frame when a beam of light travelling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? (The index of water is 4/3)Correct answer is '0.909'. Can you explain this answer?.
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