Question

The refractive indices of glass and water with respect to vaccum are 3/2 and 4/3 . If the speed of light in glass is 2x10(8) . Find the speed of light in vaccum and in water

Answer 1

SoLuTiOn :

➡ Given:

✏ Refractive index of glass and water are respectively 3/2 and 4/3

✏ Speed of light in glass is $2\times10^{8}$ m/s

➡ To Find:

1. Speed of light in vacuum.
2. Speed of light in water.

➡ Concept:

✏ Refractive index of medium is always defind as ratio of velocity of light in vacuum to the velocity of light in medium.

➡ Formula:

✏ Formula of refractive index is given by

$\star \: \underline{ \boxed{ \bold{ \mathfrak{ \pink{ \mu = \frac{velocity \: of \: light \: in \: vacuum}{velocity \: of \: light \: in \: medium}}}}}} \: \star$

➡ Calculation:

• Velocity of light in vacuum.

$\rightarrow \rm \: \mu_{g} = \frac{velocity \: of \: light \: in \: vacuum}{velocity \: of \: light \: in \: glass} \\ \\ \rightarrow \rm \: \frac{3}{2} = \frac{velocity \: of \: light \: in \: vacuum}{2 \times {10}^{8} } \\ \\ \rightarrow \rm \: \boxed{ \rm{ \red{v_{vacuum} = 3 \times {10}^{8} \: \frac{m}{s} }}} \: \star$

• Velocity of light in water.

$\rightarrow \rm \: \mu_{w} = \frac{velocity \: of \: light \: in \: vacuum}{velocity \: of \: light \: in \: water} \\ \\ \rightarrow \rm \: \frac{4}{3} = \frac{3 \times {10}^{8} }{velocity \: of \: light \: in \: water} \\ \\ \rightarrow \: \boxed{ \rm{ \blue{v_{water} = 2.25 \times {10}^{8} \: \frac{m}{s} }}} \: \star$

➡ Additional information:

• Refracrive index is unitless quantity.
• Refractive index is dimensionless quantity.