Refraction of light-apparent speed

[irunwithmonkeys]

Homework Statement

Imagine two media: one is thick air and the other is a liquid medium of some kind. The index of refraction of the air medium is 1.2
and that of the liquid medium is 1.47.
You are standing in the air medium looking straight into the liquid medium. You observe an object inside the liquid medium moving directly towards you. The speed of the object is 20 m/s. Assume the glass wall is very thin and that it doesn't affect the results. What is the apparent speed of the object as seen by you?

Homework Equations

I used c = v/n so v = c/n

The Attempt at a Solution

v=c/n= 20 [m/s] divided by 1.47 = 13.6 [m/s]

Can someone please help verify this is correct. Or am I doing this all wrong? Thank you very much for helping. I really appreciate it.

 

[rl.bhat]

v=c/n= 20 [m/s] divided by 1.47 = 13.6 [m/s] In this formula v is the velocity of the light in the medium, not the object. If T and T' are the real and apparent depths in the liquid then you can wright 1.47/T = 1.2/T'. After 1 second real depth becomes T - 20 m and apparent depth will be T' - X. Find X

 

[ogb p]

Your solution is correct. The apparent speed of the object would indeed be 13.6 m/s as seen by you in the air medium. This is because the light rays from the object are refracted as they pass from the liquid medium to the air medium, causing the object to appear closer and slower to you than it actually is. This is due to the difference in the speed of light in the two media, as described by Snell's law. Your use of the equation v = c/n, where c is the speed of light in a vacuum and n is the refractive index of the medium, is a correct approach to solving this problem. Good job!