Question

The index of refraction of diamond is 2.0, velocity of light in diamond in cm/seconds is approximately
A.) 6$ \times {10^{10}}$
B.) 3.0$ \times {10^{10}}$
C.) 2$ \times {10^{10}}$
D.) 1.5$ \times {10^{10}}$

Answer 1

Hint: The law of refraction which is generally known as Snell’s law which governs the behaviour of light rays. Speed of light c=$3 \times {10^8}$m/s is always measured in the same value. Velocity is a vector quantity that signifies the magnitude of the rate of change of position and also direction of an object movement.

Step By Step Answer:
As according to law of refraction
$\mu = \dfrac{{{V_{vacuum}}}}{{{V_{medium}}}} = \dfrac{c}{{{V_d}}} = {\mu _d}$

Here ${\mu _d}$ is (d) is the diamond so according to question

${\mu _d}$=2 (given)

And asked to find velocity of light so it will be;

${V_d} = \dfrac{c}{{{\mu _d}}}$
Where c=$3 \times {10^8}$
 $
   \Rightarrow \dfrac{{3 \times {{10}^8}}}{2}m/s \\
  1.5 \times {10^8}m/s \\
 $

We get the answer in m/s but in question it is asked in cm/s so, now we will multiply with 100

1m=100cm so we get

$1.5 \times {10^8} \times 100 = 1.5 \times {10^{10}}cm/s$

Therefore, the option D is the correct answer.

Additional Information:
2 types of law;
(i)Law associated in reflection says that the angle of incidence and reflection is equal.
(ii)Law associated with refraction says that the ratio of sine of incidence angle to sine of refraction angle is a constant term.

Don’t get confused with speed and velocity also both are different velocity can be zero but speed cannot be zero. Moreover, speed is a scalar quantity.

Note: There is a difference between refraction and reflection; In reflection the light rays follow the rebounding phenomenon of light rays in the same medium whereas in refraction the bending of light rays is towards the different mediums. Shiny surfaces are a type of reflection surface whereas transparent surfaces are a type of refraction surface.