NEET Exam  >  NEET Questions  >  A vessel is half filled with a liquid of refr... Start Learning for Free
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.?
Most Upvoted Answer
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.

Community Answer
A vessel is half filled with a liquid of refractive index u. The other...
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
Explore Courses for NEET exam

Top Courses for NEET

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.?
Question Description
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.?.
Solutions 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.? in English & in Hindi are available as part of our courses for NEET. Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of 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.? defined & explained in the simplest way possible. Besides giving the explanation of 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 detailed solution 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.? has been provided alongside types of 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.? theory, EduRev gives you an ample number of questions to practice 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.? tests, examples and also practice NEET tests.
Explore Courses for NEET exam

Top Courses for NEET

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev