Question

refractive index of a medium is 1.5. What is the velocity of light in

that medium ?
​

Answer 1

Answer:

Refractive Index is the defined as the velocity of light in vacuum divided by the velocity of light in the medium.

$\boxed{ \mu = \dfrac{ \text{Velocity of light in air} }{ \text{Velocity of light in medium} }}$

Given that, refractive index of the medium is 1.5 and the velocity of light in vacuum is 3 × 10⁸ m/s. Substituting the values we get:

$\implies 1.5 = \dfrac{3 \times 10^8}{v}\\\\\\\implies v = \dfrac{3 \times 10^8}{1.5}\\\\\\\implies \boxed{ \bf{ v = 2 \times 10^8\;\:m/s}}$

Hence the velocity of light in that medium is 2 × 10⁸ m/s.

Answer 2

Question given:

• Refractive index of a medium is 1.5. What is the velocity of light in that medium ?

Information provided with us:

• Refractive index of a medium is 1.5

What we have to calculate:

• Here we have to calculate and find out the velocity of that light in that medium.

Using Formula:

Relationship between refractive index and speed of light:-

• $\red{ \underline{ \boxed{\sf{ \mu \: = \: \frac{speed \: of \: light \: in \: air \: (c)}{speed \: of \: light \: in \: medium(V)} }}}}$

Refractive index is denoted by the symbol $\mu$

We have,

• Refractive index = 1.5
• Speed of light in air (i.e, velocity) = 3 × 10⁸

Putting the values in the formula:

$: \longmapsto \: \tt{1.5 \: = \: \dfrac{3 \times 10 {}^{8} }{V } }$

• Cross multiplying,

$: \longmapsto \: \tt{ V\: = \: \dfrac{3 \times 10 {}^{8} }{ 1.5} }$

• Now,

$: \longmapsto \: \tt{ V\: = \: \dfrac{3 \times 10 {}^{8} \times 10}{ 15} }$

• On cancelling them,

$: \longmapsto \: \tt{ V\: = \: \dfrac{3 \times 10 {}^{8} \times \cancel{10}}{ \cancel{15}} }$

$: \longmapsto \: \tt{ V\: = \: \dfrac{3 \times 10 {}^{8} \times 2}{ 3} }$

$: \longmapsto \: \tt{ V\: = \: \dfrac{ \cancel3 \times 10 {}^{8} \times 2}{ \cancel3} }$

$: \longmapsto \: \pink{\underline{\boxed{\tt{ V\: = \: 2 \times 10 {}^{8} }}}}$

$\small{ \underline{ \bf{Therefore, \: velocity \: of \: light \: in \: that \: medium \: is \: of \: 2 \times 10 {}^{8}}}}$

Additional Information:

Refractive index of some substances:-

• Vacuum = 1.00
• Alcohol = 1.37
• Ruby = 1.76
• Diamond = 2.41
• Ordinary glass = 1.5
• kerosene = 1.41
• Glycerine = 1.47

Remember that:-

• Speed of light always greater in vacuum
• Speed of light i.e., velocity is denoted by c
• Refractive index doesn't have any unit
• Refractive index of a transparent medium is more than one. (i.e., greater)