Question

calculate refractive index of Glass with respect to water if speed of light in glass is 2×10^8m/s and in water it is 2.25×10^8m/s.​

Answer 1

Given:

Speed of light in glass, v₁= 2×10⁸ m/s

Speed of light in water, v₂= 2.25×10⁸ m/s

To Find:

Refractive index of Glass with respect to water

Solution:

We know that,

• Relation between refractive index and speed of light for two medium is given by

$\pink{\boxed{\bf{\dfrac{n_{1}}{n_{2}}=\dfrac{v_{2}}{v_{1}}}}}$

where,

n₁ is refractive index of first medium

n₂ is refractive index of second medium

v₁ is velocity of light in first medium

v₂ is velocity of light in second medium

• $\pink{\boxed{\bf{n_{12}=\dfrac{n_{1}}{n_{2}}}}}$

where,

n₁₂ is refractive index of first medium with respect to second medium

n₁ is refractive index of first medium

n₂ is refractive index of second medium

$\rule{190}{1}$

Let the refractive of glass be n₁, refractive index of water be n₂ and refractive index of glass with respect to water be n₁₂

So,

$\longrightarrow\rm{n_{12}=\dfrac{n_{1}}{n_{2}}}-------(1)$

$\longrightarrow\rm{\dfrac{n_{1}}{n_{2}}=\dfrac{v_{2}}{v_{1}}}--------(2)$

From (1) and (2), we get

$\longrightarrow\rm{n_{12}=\dfrac{v_{2}}{v_{1}}}$

$\longrightarrow\rm{n_{12}=\dfrac{2.25\times10^{8}}{2\times10^{8}}}$

$\longrightarrow\rm\green{n_{12}=1.125}$

Hence, the refractive index of glass with respect to water is 1.125.