Question

The speed of light changes when it goes from ethyl alcohol (nea = 1.389) to carbon tetrachloride (nct = 1.436). What is the ratio vct vea of the speeds?

Answer 1

The ratio of the velocity of carbon tetra chloride and ethyl alcohol is 0.96.

Step-by-step explanation:

Given that,

Refractive index of ethyl alcohol n= 1.389

Refractive index of carbon tetra chloride n'= 1.436

We need to calculate the ratio of the velocity of carbon tetra chloride and ethyl alcohol

Using formula of velocity

`(v')/(v)=(n)/(n')`

Where, n= refractive index of ethyl alcohol

n'=refractive index of carbon tetra chloride

Put the value into the formula

`(v')/(v)=(1.389)/(1.436)`

`(v')/(v)=(1389)/(1436)`

`(v')/(v)=0.96`

Hence, The ratio of the velocity of carbon tetra chloride and ethyl alcohol is 0.96.

Answer 2

`n_(ca)=(v_(ct))/(v_(ea))` is the refractive index of ethyl alcohol with respect to carbon tetrachloride.

Step-by-step explanation:

Given;

refractive index of ethyl alcohol,
`n_(ea)=1.389`

refractive index of carbon tetra-chloride,
`n_(ct)=1.436`

As we know that the refractive index of any medium is given as:

`\rm n_(ea)=(speed\ of\ light\ in\ the\ air)/(speed\ of\ light\ in\ the\ medium) =(c)/(v_(ea))` ........................(1)

&

`n_(ct)=(speed\ of\ light\ in\ the\ air)/(speed\ of\ light\ in\ the\ carbon\ tetrachloride) =(c)/(v_(ct))` ..............................(2)

Now, divide eq. 1 by eq. 2:

`n_(ca)=(c)/(v_(ea)) / (c)/(v_(ct))`

`n_(ca)=(v_(ct))/(v_(ea))` is the refractive index of ethyl alcohol with respect to carbon tetrachloride.