Question

Velocity of light in water, glass and vacuum have the values \[{{V}_{w}}\], \[{{V}_{g}}\] and \[{{V}_{c}}\] respectively. Which of the following relations is true?
(A). \[{{V}_{w}}={{V}_{g}}={{V}_{c}}\]
(B). \[{{V}_{w}}>{{V}_{g}}\text{ but }{{V}_{w}}<{{V}_{c}}\]
(C). \[{{V}_{w}}={{V}_{g}}\text{ but }{{V}_{w}}<{{V}_{c}}\]
(D). \[{{V}_{c}}>{{V}_{w}}\text{ but }{{V}_{w}}<{{V}_{g}}\]

Answer 1

Hint: The velocity of the light in a medium is dependent on the refractive index. These are in an inverse relationship. So, if the refractive index is more, then the velocity of the light will be smaller.

Complete step by step answer:
As we know, the refractive index of any medium is the ratio of the velocity of light in a vacuum to the velocity of light in a substance at the same wavelength. It is depending on the density of the medium through which the light is travelling and the wavelength of the light.
\[n=\dfrac{c}{v}\], where n is the refractive index, c is the velocity of the light in vacuum and v is the velocity of the light in a particular substance. Here we can see the velocity of the light is in an inverse relationship with the refractive index. So if the velocity increases the refractive index decreases. The vacuum has a minimum refractive index. It is considered as 1. So all other substances have an index of refraction more than that. According to the refractive index ascending order, the given mediums can be arranged as,
\[\Rightarrow {{n}_{c}}<{{n}_{w}}<{{n}_{g}}\]
That means the velocity of the light in these mediums is in the opposite order of the refractive index.
\[{{V}_{w}}>{{V}_{g}}\text{ but }{{V}_{c}}>{{V}_{w}}\]
Therefore the correct option is B. The velocity of the light will be maximum at vacuum. The medium of water and glass will be second and third position in that list.

Additional information:
Snell’s law also can be used to find the refractive index value. According to this, If the light is moving from one medium to another, the index of refraction will be the ratio of the sine of the angle of incidence to the angle of refraction.
\[n=\dfrac{\sin i}{\sin r}\]
Isotropic minerals have a single refractive index value since the optical properties will be the same in all directions. For anisotropic materials, optical properties will not be the same in all directions. Thus, it has more than two refractive indices.

Note: It is better to remember the refractive index values of glass, water and air. Since these are very important in the optics. Moreover, these mediums are very common to us.
For water, the refractive index will be 1.33.
For glass, the refractive index will be 1.5.
For air, the refractive index will be 1.
As we discussed earlier, the minimum refractive index is of air.