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In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x 104 ms−1 , the number of rotations made by the rotating mirror in one minute are
- a)3,000
- b)9,000
- c)18,000
- d)36,000
Correct answer is option 'C'. Can you explain this answer?
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In Foucaults rotating mirror experiment to determine the velocity of l...
Degrees. The speed of light in air can be calculated as follows:
First, we need to calculate the time it takes for the light to travel from the rotating mirror to the concave mirror and back. This can be done using the formula:
time = distance / speed
where distance is twice the distance from the rotating mirror to the concave mirror (i.e. 2 x 6000 = 12000 metres), and speed is the speed of light in air (which we want to find).
Let's assume that the time taken is t seconds.
Next, we need to calculate the angle through which the mirror rotates in this time. The mirror rotates at a constant speed, so we can use the formula:
angle = angular velocity x time
where angular velocity is the speed of rotation of the mirror (which is not given in the question, but let's assume it is known).
Let's assume that the angle of rotation is A degrees.
Now, we can use the formula for the displacement of the reflected ray:
displacement = 2 x distance x tan(angle/2)
where distance is the distance from the rotating mirror to the concave mirror (i.e. 6000 metres), and angle is the angle of rotation of the mirror (in radians).
We need to convert the angle from degrees to radians:
A (in radians) = A (in degrees) x pi / 180
Substituting the values we have:
displacement = 2 x 6000 x tan(A/2 x pi/180)
= 12000 x tan(A/360 x pi)
= 12000 x tan(48/360 x pi)
= 12000 x tan(0.133)
= 12000 x 0.135
= 1620 metres
Finally, we can use the formula for the speed of light in air:
speed = displacement / time
Substituting the values we have:
speed = 1620 / t
We need to solve for t, which we can do by equating the formulas for time and displacement:
time = displacement / (2 x distance x tan(angle/2))
Substituting the values we have:
t = 1620 / (2 x 6000 x tan(A/2 x pi/180))
= 1620 / (2 x 6000 x tan(48/2 x pi/180))
= 1620 / (2 x 6000 x tan(24/180 x pi))
= 1620 / (2 x 6000 x 0.455)
= 0.035 seconds
Substituting the value of t into the formula for speed:
speed = 1620 / 0.035
= 46286 metres per second
Therefore, the speed of light in air is approximately 46,286 metres per second.
First, we need to calculate the time it takes for the light to travel from the rotating mirror to the concave mirror and back. This can be done using the formula:
time = distance / speed
where distance is twice the distance from the rotating mirror to the concave mirror (i.e. 2 x 6000 = 12000 metres), and speed is the speed of light in air (which we want to find).
Let's assume that the time taken is t seconds.
Next, we need to calculate the angle through which the mirror rotates in this time. The mirror rotates at a constant speed, so we can use the formula:
angle = angular velocity x time
where angular velocity is the speed of rotation of the mirror (which is not given in the question, but let's assume it is known).
Let's assume that the angle of rotation is A degrees.
Now, we can use the formula for the displacement of the reflected ray:
displacement = 2 x distance x tan(angle/2)
where distance is the distance from the rotating mirror to the concave mirror (i.e. 6000 metres), and angle is the angle of rotation of the mirror (in radians).
We need to convert the angle from degrees to radians:
A (in radians) = A (in degrees) x pi / 180
Substituting the values we have:
displacement = 2 x 6000 x tan(A/2 x pi/180)
= 12000 x tan(A/360 x pi)
= 12000 x tan(48/360 x pi)
= 12000 x tan(0.133)
= 12000 x 0.135
= 1620 metres
Finally, we can use the formula for the speed of light in air:
speed = displacement / time
Substituting the values we have:
speed = 1620 / t
We need to solve for t, which we can do by equating the formulas for time and displacement:
time = displacement / (2 x distance x tan(angle/2))
Substituting the values we have:
t = 1620 / (2 x 6000 x tan(A/2 x pi/180))
= 1620 / (2 x 6000 x tan(48/2 x pi/180))
= 1620 / (2 x 6000 x tan(24/180 x pi))
= 1620 / (2 x 6000 x 0.455)
= 0.035 seconds
Substituting the value of t into the formula for speed:
speed = 1620 / 0.035
= 46286 metres per second
Therefore, the speed of light in air is approximately 46,286 metres per second.
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In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x104 ms−1 , the number of rotations made by the rotating mirror in one minute area)3,000b)9,000c)18,000d)36,000Correct answer is option 'C'. Can you explain this answer?
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In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x104 ms−1 , the number of rotations made by the rotating mirror in one minute area)3,000b)9,000c)18,000d)36,000Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x104 ms−1 , the number of rotations made by the rotating mirror in one minute area)3,000b)9,000c)18,000d)36,000Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x104 ms−1 , the number of rotations made by the rotating mirror in one minute area)3,000b)9,000c)18,000d)36,000Correct answer is option 'C'. Can you explain this answer?.
In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x104 ms−1 , the number of rotations made by the rotating mirror in one minute area)3,000b)9,000c)18,000d)36,000Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x104 ms−1 , the number of rotations made by the rotating mirror in one minute area)3,000b)9,000c)18,000d)36,000Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In Foucaults rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π x 10−2 radians. If the velocity of light in air is 3 x104 ms−1 , the number of rotations made by the rotating mirror in one minute area)3,000b)9,000c)18,000d)36,000Correct answer is option 'C'. Can you explain this answer?.
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