Find Refractive Index of Liquid for Observer with Velocity

In summary, the conversation revolves around a question about finding the refractive index of a liquid for an observer with a given velocity. The individual has a solution, but it is pointed out that there is an error in the calculation. The individual asks for clarification and the expert explains the error and encourages them to check their work. The individual makes corrections and thanks the expert for their help.
  • #1
Paul Black
28
0
hello

i have this question
" a liquid has refractive index (n). find the refractive index of this liquid for an observer if the liquid have a velocity (v) to this observer "

i have my solution in an attachment
please look at it and tell me if it is the right solution

thank you very much
 

Attachments

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  • #2
Paul Black said:
hello

i have this question
" a liquid has refractive index (n). find the refractive index of this liquid for an observer if the liquid have a velocity (v) to this observer "

i have my solution in an attachment
please look at it and tell me if it is the right solution

thank you very much

The approach is correct up to the point where you make a mistake in the calculation of [itex]v'_x[/itex]. The formula that you use is incorrect, look at the term [itex]1-\frac{v^2}{c^2} v_x[/itex], what you want is [itex]1-\frac{vv_x}{c^2} [/itex]
 
Last edited:
  • #3
sorry but i don't get it.
can you explain it more. i thought my formula is correct
or is there something is forget?
what about the rest of the solution

please if you have time, can you give me the complete solution to this question
i have tomorrow an exam and i have no time
please do me this favor
thank you very much
 
  • #4
Paul Black said:
sorry but i don't get it.
can you explain it more. i thought my formula is correct

No, it isn't.

what about the rest of the solution

Once you make this error, everything else becomes incorrect. You need to learn how to check your own work, especially after your errors are pointed out to you.

please if you have time, can you give me the complete solution to this question
i have tomorrow an exam and i have no time
please do me this favor
thank you very much

We do not do your homework for you, you don't learn anything if I do it for you. I gave you the exact error in your derivation, your speed composition formula is wrong and I pointed out your exact error.
 
  • #5
To add to what xox has already said. Your end result cannot be correct on dimensional grounds. Dimensional analysis is always a good check to see if your result makes sense. In your case you are subtracting a velocity squared from a velocity in the numerator. Since velocity has dimension length/time, velocity^2 has dimension length^2/time^2 and you cannot add or subtract quantities of different dimensions.
 
  • #6
omg that is so embarrassing
sorry but I am out of time. that's is the reason for my stupid mistake
i get it and have again my solution in an attachment


We do not do your homework for you, you don't learn anything if I do it for you. I gave you the exact error in your derivation, your speed composition formula is wrong and I pointed out your exact error.

yes you are soooo right.

thank you again
 

Attachments

  • CCI05282014_00001.jpg
    CCI05282014_00001.jpg
    9.2 KB · Views: 407
  • #7
Paul Black said:
omg that is so embarrassing
sorry but I am out of time. that's is the reason for my stupid mistake
i get it and have again my solution in an attachment




yes you are soooo right.

thank you again

It is better but you still have algebraic errors. Check your work.
 
  • #8
i checked it but didnt find any errors
 
  • #9
Paul Black said:
i checked it but didnt find any errors

Yes, it is right now.
 
  • #10
Ok. Thank you for your help
 

1. What is the purpose of finding the refractive index of a liquid for an observer with velocity?

The refractive index of a liquid for an observer with velocity is used to determine how light travels through the liquid for an observer who is also moving. This is important in understanding how light behaves in different conditions, such as when viewed from a moving vehicle or in experiments involving liquids in motion.

2. How do you measure the refractive index of a liquid for an observer with velocity?

To measure the refractive index of a liquid for an observer with velocity, you can use a refractometer. This device measures the angle of refraction of light passing through the liquid for an observer with a known velocity, and calculates the refractive index based on this measurement. Alternatively, you can also use the formula n = c / v, where n is the refractive index, c is the speed of light in a vacuum, and v is the velocity of the observer.

3. What factors can affect the refractive index of a liquid for an observer with velocity?

The refractive index of a liquid for an observer with velocity can be affected by various factors. These include the temperature and pressure of the liquid, as well as the velocity and direction of the observer. Additionally, the composition and density of the liquid can also impact its refractive index for an observer with velocity.

4. How is the refractive index of a liquid for an observer with velocity related to the speed of light?

The refractive index of a liquid for an observer with velocity is directly related to the speed of light in the liquid. This means that as the speed of light increases, the refractive index also increases. Conversely, as the speed of light decreases, the refractive index decreases. This relationship is described by the equation n = c / v, where n is the refractive index, c is the speed of light in a vacuum, and v is the velocity of the observer.

5. Can the refractive index of a liquid for an observer with velocity be greater than 1?

Yes, the refractive index of a liquid for an observer with velocity can be greater than 1. In fact, most liquids have a refractive index greater than 1. This is because light travels slower in liquids than it does in a vacuum, which has a refractive index of 1. The refractive index of a liquid for an observer with velocity can vary depending on the properties of the liquid and the velocity of the observer.

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