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

In summary, the ratio of the speed of light in ethyl alcohol (n=1.36) to the speed of light in benzene (n=1.50) is 1.10. If light travels for 3.0ns in ethyl alcohol, it will travel 1.10 times further in ethyl alcohol than in benzene. This is equivalent to 3.3 x 10^-9 m/s faster in ethyl alcohol than in benzene.
  • #1
tangowhiskey
4
0
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 don't 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
 
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  • #2
tangowhiskey said:
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 don't 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
 
  • #3
SteamKing said:
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 I am wrong but it might be

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

now I am unclear about what to do..
 
  • #4
tangowhiskey said:
correct me if I am wrong but it might be

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

now I am 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.
 
  • #5
SteamKing said:
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

??
 
  • #6
tangowhiskey said:
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?
 
  • #7
SteamKing said:
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
 

1. How does ethyl alcohol affect the speed of light?

The speed of light in a medium, such as ethyl alcohol, is determined by the refractive index of the substance. Ethyl alcohol has a refractive index of 1.36, which is higher than that of air (1.00), meaning that light travels slower in ethyl alcohol than in air.

2. Is the speed of light constant in all substances?

No, the speed of light is not constant in all substances. It depends on the refractive index of the substance, which is determined by its density and composition.

3. How is the speed of light in ethyl alcohol measured?

The speed of light in ethyl alcohol (or any other substance) can be measured using a variety of techniques, such as the use of prisms, interferometers, or spectroscopy.

4. How does the speed of light in ethyl alcohol compare to other substances?

The speed of light in ethyl alcohol is slower than in air, but faster than in other substances with higher refractive indices, such as water (1.33) or diamond (2.42).

5. Why is the speed of light in ethyl alcohol important to know?

Knowing the speed of light in ethyl alcohol (or any other substance) is important for understanding the behavior of light in various mediums, as well as for practical applications such as designing optical devices and assessing the purity of substances.

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