# The refractive index for an observer

1. May 28, 2014

### Paul Black

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

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2. May 28, 2014

### xox

The approach is correct up to the point where you make a mistake in the calculation of $v'_x$. The formula that you use is incorrect, look at the term $1-\frac{v^2}{c^2} v_x$, what you want is $1-\frac{vv_x}{c^2}$

Last edited: May 28, 2014
3. May 28, 2014

### Paul Black

sorry but i dont 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
thank you very much

4. May 28, 2014

### xox

No, it isn't.

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.

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. May 28, 2014

### Orodruin

Staff Emeritus
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. May 28, 2014

### Paul Black

omg that is so embarrassing
sorry but im out of time. thats 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

#### Attached Files:

• ###### CCI05282014_00001.jpg
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Views:
94
7. May 28, 2014

### xox

It is better but you still have algebraic errors. Check your work.

8. May 28, 2014

### Paul Black

i checked it but didnt find any errors

9. May 28, 2014

### xox

Yes, it is right now.

10. May 28, 2014

### Paul Black

Ok. Thank you for your help