Question

The speed of light in a piece of crown glass is $2\, \times \,{10^5}{\text{m/s}}$ . Find out the refractive index of crown glass?
A) $2$
 B) $1500$
 C) $0.67$
 D) $0.33$
 E) $0.2$

Answer 1

Hint:Refractive index which is also called as index of refraction or refraction index is a dimensionless number which tells us how fast light travels through a particular material and mathematically it is defined as $n\, = \,\dfrac{c}{v}$ .

Step by step solution:
From the question it is given that the speed of light in crown glass (v) = $2\, \times \,{10^5}{\text{m/s}}$ .
Also, we already know that the speed of light in vacuum (c) = $3\, \times \,{10^8}{\text{m/s}}$ .
Now applying refractive index formula
${\text{Refractive index (n)}}\,{\text{ = }}\dfrac{{{\text{speed of light in vacuum(c)}}}}{{{\text{speed of light in given medium(v)}}}}$
Putting these values in above equation, ${\text{Refractive index (n)}}\,{\text{ = }}\dfrac{{3\, \times \,{{10}^8}}}{{2\, \times \,{{10}^5}}}$
Solving above equation we get ${\text{Refractive index (n)}}\,{\text{ = 1}}{\text{.5}}\, \times \,{\text{1}}{{\text{0}}^3}\, = \,1500$

Therefore, option B is the correct answer

Additional Information:
As per Snell's law of refraction, ${n_1}\,\sin {\theta _1}\, = \,{n_2}\sin {\theta _2}$ where ${\theta _1}$ and ${\theta _2}$ are the angles of incidence and refraction, respectively, of a ray crossing the interface between two media with refractive indices ${n_1}$ and ${n_2}$ . Refractive indices also determine how much light get reflected when it reaches a particular interface as well as it also determines the critical angle of total internal reflection. We should also note that refractive index also varies with wavelength which is the also the reason behind white light to split into its constituent colors when it is refracted.

Note: Refractive index of $1500$ in the above solution would actually mean that light travels $1500$ times faster in vacuum as it travels in crown glass. We should also note that air and vacuum refractive index are different, refractive index of vacuum is $1$ whereas refractive index of air is $1.0003$ . We should also remember a few refractive indexes for faster calculation such as refractive index for water is $1.33$ and for diamond its $2.417$ .