Question

The speed of light in a block of glass is found to be 1.90x10 8 m/s. Calculate the refractive index of
the glass.

Answer 1

Given that:

• Speed of light in block of glass = 1.90 × 10⁸ mps

To calculate:

• Refractive index

Solution:

• Refractive index = 1.57

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.

Knowledge required:

• Speed of light in air = 3 × 10⁸ mps

Required solution:

$:\implies \sf n \: = \dfrac{c}{v} \\ \\ :\implies \sf n \: = \dfrac{3 \times 10^8}{1.90 \times 10^8} \\ \\ :\implies \sf n \: = \dfrac{3 \times \cancel{10^8}}{1.90 \times \cancel{10^8}} \: (Cancelling) \\ \\ :\implies \sf n \: = \dfrac{3}{1.90} \\ \\ :\implies \sf n \: = \dfrac{300}{190} \\ \\ :\implies \sf n \: = \dfrac{30}{19} \\ \\ :\implies \sf n \: = 1.57$

• Henceforth, 1.57 is refractive index.

Additional information:

$\begin{gathered}\boxed{\begin{array}{c|cc}\bf Substance &\bf Speed_{(sound)} \: in \: ms^{-1} \\\frac{\quad \quad \quad\quad\quad \quad\quad\quad}{}&\frac{\quad \quad \quad\quad\quad \quad\quad\quad}{}\\\sf Alluminium &\sf 6420 \\ \\ \sf Brass & \sf 4700 \\ \\ \sf Steel & \sf 5960 \\ \\ \sf Iron & \sf 5950 \\ \\ \sf Glass & \sf 3980 \\ \\ \sf Oxygen & \sf 316 \\ \\ \sf Air & \sf 346 \end{array}}\end{gathered}$