Question

Refractive index of glass with respect to air is 1.5 and refractive index of water with respect to air is 4/3 .What will be the ratio of speed of light in water to speed of light in glass ?

Answer 1

Answer:

Explanation:

The formula for the refractive index of a medium is given by

n = c/v

Where,

c = speed of light in vacuum

v = speed of light in that medium

n  = refractive index

Thus,

n glass = speed of light in vacuum/ speed of light in glass

n water= speed of light in vacuum/ speed of light in water

Since, we need to find the ratio. We will get,

n glass /n water = (speed of light in vacuum/ speed of light in glass) x (speed of light in water/ speed of light in vacuum)

Thus,

n glass / n water = speed of light in water / speed of light in glass

So, after substituting values

Speed of light in water/ speed of light in glass = 3/2 x 3/4 = 1.125

Answer 2

Given:

The refractive index of glass with respect to air, μ (a/g) = 1.5

The refractive index of water with respect to air, μ (a/w) = 4/3 = 1.33

To Find:

The ratio of speed of light in water to the speed of light in glass, i.e., v(w) / v(g).

Calculation:

- We know that:

Refractive index = Speed of light in vacuum / Speed of light in medium

⇒ μ (a/g) = Speed of light in vacuum / Speed of light in glass ....(i)

⇒ μ (a/w) = Speed of light in vacuum / Speed of light in water ....(ii)

- Dividing (i) by (ii), we get:

μ (a/g) /  μ (a/w) = Speed of light in water / Speed of light in glass

⇒ v(w) / v(g) = 1.5 / 1.33

⇒ v(w) / v(g) = 1.128

- So, the ratio of speed of light in water to the speed of light in glass is 1.128.