Question

The refractive index of glycerin is 1.46 then what is the speed of light in air if it's speed in glycerin is 2.05x10^8m/s

Answer 1

SoLuTiOn :

⏭ Given:

✏ Refractive index of glycerin = 1.46

✏ Velocity of light in glycerin = $2.05\times10^{8}$ m/s

⏭ To Find:

✏ Velocity of light in air ?

⏭ Concept:

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

⏭ Formula:

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

⏭ Calculation:

$\mapsto \sf \: \mu_{glass} = \frac{velocity \: of \: light \: in \: air}{velocity \: of \: light \: in \: glass} \\ \\ \mapsto \sf \: 1.46 = \frac{v_{air}}{2.05 \times {10}^{8} } \\ \\ \mapsto \: \underline{ \boxed{ \bold{ \sf{ \purple{v_{air} = 3 \times {10}^{8} \: m {s}^{ - 1} }}}}} \: \orange{ \bigstar}$

⏭ Additional information:

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

Answer 2

Answer:

The refractive index of glycerin is 1.46.  The speed in glycerin is 2.05x10^8m/s. Then the speed of light in the air will be $3\times10^{8} \ m/s$

Explanation:

The expression for refractive index (μ) is given by,

$\\\mu = \frac {c}{v}$  

Where c is the speed of light in the vacuum and v is the velocity of light in a medium.

Or,

${c}= v\times{\mu$                 ...(1)

In this problem, the medium is glycerin.

From the question,

$v= 2.05\times10^{8} m/s$          $\mu = 1.46$        $c= ?$

Substitute these values into equation (1),

${c}= 2.05\times10^8\times1.46 = 2.9930\times 10^8\ m/s$

Thus the speed of light in air $= 2.9930\times 10^8\ m/s$ ≅ $3\times10^{8} \ m/s$