Question

The speed of light in turpentine oil is $2 \times {10^8}$ m/s. The absolute refractive index of oil is about…. ?[Speed of light in vacuum $\approx$ $3 \times {10^8}$ m/s.]
A) 1.5
B) 2
C) 1.3
D) 0.67

Answer 1

Speed of light varies from medium to medium. For example, if a ray of light is travelling in water the speed of light will be different than when the same ray of light is travelling in the air. This difference is because of the medium in which the light is travelling. To understand this variation in speed of light in the different mediums we compare the speed of speed in a medium with the speed of light in a vacuum by taking their ratio. This ratio is called the absolute refractive index. In the question, we are given the speed of light in a medium, which is turpentine oil, and speed of light in a vacuum. We will calculate the ratio to reach the correct answer.

Complete step by step solution:
Step 1: Express the formula for the absolute refractive index for a medium
${\eta _o} = \dfrac{{{v_o}}}{c}$
Where ${\eta _o}$is the absolute refractive index of the turpentine oil, ${v_o}$ is the speed of light in the oil and $c$ is the speed of light in the vacuum.

Step 2: Now substitute the value $2 \times {10^8}$ m/s for ${v_o}$ and $3 \times {10^8}$ m/s for $c$ .
$\therefore {\eta _o} = \dfrac{{2 \times {{10}^8}}}{{3 \times {{10}^8}}}$

Step 3: ${10^8}$ will be cancelled out and divided 2 by 3 and you will get the correct answer.
$\therefore {\eta _o} = 0.66666$
This value is almost equal to 0.67.

Hence, the correct option is D.

Note: The speed of light is maximum in a vacuum. Therefore, the value of ${\eta _o}$ is always 1 or less than 1 but not greater than 1. Now, we can see that in options A, B and C the value of ${\eta _o}$ is greater than 1 and hence these options can not be correct.
While calculating the absolute refractive index of a medium we should remember that the value of the speed of light in the medium should be put in the numerator and not in the denominator. Absolute refractive index has no unit.