Q 1.If the refractive index of water for light going from air to water be 1.33 , what will be the refractive index for light going from water to air

Solution:
We know the relation of refractive index for the two set of media.

Here air is the first medium and water is second medium. For these two set of media we can write the formula as given below.

_{water} μ _{air} = 1 / _{air} μ _{water}

Here given

_{air} μ _{water} = 1.33

∴ _{water} μ _{air} = 1 / 1.33

or _{water} μ _{air} = 0.75 __Ans.__

Q 2. The refractive indices of kerosene turpentine and water are 1.44 , 1.47 and 1.33 respectively . In which of these materials does the light travels fastest?

Solution:
We know:
R.I.= Speed of light in air / Speed of the light in the medium

Let

Speed of light in air=v_{a}

Speed of light in Kerosine = v _{k}

Speed of light in Turpentine = v _{t}

and Speed of light in Water = v _{w}

Given :

v _{k} = 1.44

v _{t} = 1.47

and v _{w} = 1.33

Therefore for kerosene we can write,

R. I. of kerosene (_{a} μ _{k} ) = v _{a} / v _{k}

or v _{k} = v _{a} / _{a} μ _{k}

∴ v _{k} = v _{a} / 1.44 - - - - - (1)

for turpentine we can write,

R. I. of kerosene (_{a} μ _{t} ) = v _{a} / v _{t}

v _{t} = v _{a} / _{a} μ _{t}

∴ v _{t} = v _{a} / 1.47 - - - - - (2)

for water we can write,

R. I. of kerosene (_{a} μ _{w} ) = v _{a} / v _{w}

v _{w} = v _{a} / _{a} μ _{w}

∴ v _{w} = v _{a} / 1.33 - - - - - (3)

All the three equation have v _{a} as common numerator.

We also know that velocity of the medium is inversally proportional to R.I.

As the R.I. of water is lowest

therefore the velocity of the light will be highest in water. Ans.

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