# If light travels for 3.0ns in ethyl alcohol, how much furthe

Ratio is 1.10 for part 1.
1. Determine the ratio for the speed of light in ethyl alcohol (n=1.36) to the speed of light in benzene (n=1.50).

2. If light travels for 3.0ns in ethyl alcohol, how much further will it travel in this material than it would in benzene? answer will be in terms of speed of light in benzene, Vbenzene.

here is my work for part 2 but i dont think its right,

for part 2 knowing Ve/Vb = 1.10

d=Vet

Vc=(1.10)Vb
d=Vet
Ve=(1.10)Vb
de=(1.1)Vbt
de=(3.0x10^9s)Vb

d=1.10Vb x 3.0x10^-3

d=1.10 x 3x10^-3 Vb

Vb(3x10^-9) = d

## Answers and Replies

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
Ratio is 1.10 for part 1.
1. Determine the ratio for the speed of light in ethyl alcohol (n=1.36) to the speed of light in benzene (n=1.50).

2. If light travels for 3.0ns in ethyl alcohol, how much further will it travel in this material than it would in benzene? answer will be in terms of speed of light in benzene, Vbenzene.

here is my work for part 2 but i dont think its right,

for part 2 knowing Ve/Vb = 1.10

d=Vet

Vc=(1.10)Vb
d=Vet
Ve=(1.10)Vb
de=(1.1)Vbt
de=(3.0x10^9s)Vb

d=1.10Vb x 3.0x10^-3

d=1.10 x 3x10^-3 Vb

Vb(3x10^-9) = d
Your final result doesn't make any sense. All you've done is multiply Vb by 3 ns. The question asks how much further does light travel in ethyl alcohol in 3 ns than it does in the same time in benzene.

What's the definition of the index of refraction n of a material, in terms of the speed of light c?

https://en.wikipedia.org/wiki/Refractive_index

Your final result doesn't make any sense. All you've done is multiply Vb by 3 ns. The question asks how much further does light travel in ethyl alcohol in 3 ns than it does in the same time in benzene.

What's the definition of the index of refraction n of a material, in terms of the speed of light c?

https://en.wikipedia.org/wiki/Refractive_index
correct me if im wrong but it might be

speed of light in benzene (3x10^8)/(1.50) = 2x10^8 m/s

now im unclear about what to do..

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
correct me if im wrong but it might be

speed of light in benzene (3x10^8)/(1.50) = 2x10^8 m/s

now im unclear about what to do..
Well, you know (I hope) that distance traveled = speed × time.

In step 1, you calculated the ratio of the indices of refraction for ethyl alcohol to benzene and found that ratio to be about 1.10. This is how much faster light travels thru ethyl alcohol than benzene. Over 3 ns, how much farther does light travel thru ethyl alcohol than benzene? "How much farther" means what's the difference in distance traveled in the two liquids during the same amount of time.

Well, you know (I hope) that distance traveled = speed × time.

In step 1, you calculated the ratio of the indices of refraction for ethyl alcohol to benzene and found that ratio to be about 1.10. This is how much faster light travels thru ethyl alcohol than benzene. Over 3 ns, how much farther does light travel thru ethyl alcohol than benzene? "How much farther" means what's the difference in distance traveled in the two liquids during the same amount of time.

so then

d = (1.10)(3x10^-9) = 3.3 x 10^-9 seconds

??

SteamKing
Staff Emeritus
Science Advisor
Homework Helper
so then

d = (1.10)(3x10^-9) = 3.3 x 10^-9

??
No, you're not even writing out the units with your calculations, which you should always do. Remember, 1.10 is a ratio; it is unitless. If you multiply a ratio by a velocity, you're going to get another velocity, not a distance.

In this case, perhaps making a simple sketch would help you visualize what's happening.

Pretend you have two containers, one filled with ethyl alcohol and the other filled with benzene. How would you show the distance light travels thru each container in 3 ns? How would you show the difference in the distance light traveled in each fluid?

No, you're not even writing out the units with your calculations, which you should always do. Remember, 1.10 is a ratio; it is unitless. If you multiply a ratio by a velocity, you're going to get another velocity, not a distance.

In this case, perhaps making a simple sketch would help you visualize what's happening.

Pretend you have two containers, one filled with ethyl alcohol and the other filled with benzene. How would you show the distance light travels thru each container in 3 ns? How would you show the difference in the distance light traveled in each fluid?

my physics is too poor to figure this out