Question

Speed of light in air is 3×108 m/s, and 1.8×108 m/s in certain medium, what is the refractive index of that medium?​

Answer 1

Provided that:

• Speed of light in air = 3 × 10⁸ mps

• Speed of light in other medium = 1.8 × 10⁸ mps

To calculate:

• Refractive index

Solution:

• Refractive index = 1.66

Using concept:

• Refractive index formula

Using formula:

${\small{\underline{\boxed{\pmb{\sf{\longmapsto \: n \: = \dfrac{c}{v}}}}}}}$

Where, n denotes Refractive index, c denotes speed of light in air or vaccume and v denotes speed of light in other medium.

Required solution:

$:\implies \sf n \: = \dfrac{c}{v} \\ \\ :\implies \sf n \: = \dfrac{3 \times 10^8}{1.8 \times 10^8} \\ \\ :\implies \sf n \: = \dfrac{3 \times \cancel{10^8}}{1.8 \times \cancel{10^8}} \: (Cancelling) \\ \\ :\implies \sf n \: = \dfrac{3}{1.8} \\ \\ :\implies \sf n \: = \dfrac{30}{18} \\ \\ :\implies \sf n \: = \dfrac{15}{9} \\ \\ :\implies \sf n \: = \dfrac{5}{3} \\ \\ :\implies \sf n \: = 1.66 \\ \\ :\implies \sf Refractive \: index \: = 1.66$