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A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.?
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A vessel is half filled with a liquid of refractive index u. The other...
Explanation:
- Let the actual depth of the vessel be h.
- The upper half of the vessel is filled with a liquid of refractive index u.
- The lower half of the vessel is filled with an immiscible liquid of refractive index 1.5u.
- Let the depth of the upper half of the vessel be x. So, the depth of the lower half of the vessel is h-x.
- According to the question, the apparent depth of the vessel is 50% of the actual depth.
- So, the apparent depth of the vessel is h/2.
- Using the formula for apparent depth, we get:
Apparent Depth = Actual Depth / Refractive Index
h/2 = x/u + (h-x)/1.5u
- On solving this equation, we get:
h = 3x
- Now, we need to find the value of u.
- Using Snell's law, we can write:
u sin θ1 = 1.5u sin θ2
- Since the angle of incidence and angle of refraction are complementary, we have:
sin θ1 = cos θ2
- Substituting this in the above equation, we get:
u cos θ2 = 1.5u sin θ2
- Dividing both sides by sin θ2, we get:
cot θ2 = 1.5
- Using the formula for refractive index, we have:
u = sin θ1
- Using the relation between angle of incidence and angle of refraction, we get:
sin θ1 = sin(90-θ2) = cos θ2
- Substituting this in the above equation, we get:
u = cot θ2 / 1.5 = 2/3
- Therefore, the value of u is 2/3.
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A vessel is half filled with a liquid of refractive index u. The other...
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A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.?
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A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.?.
A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel is half filled with a liquid of refractive index u. The other half of the vessel is filled with an immiscible liquid of refractive index1.5u. The apparent depth of vessel is 50% of the actual depth. The value of u is.?.
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