Question

The refractive indices of water, glass, kerosene and diamond are 1.33, 1.5, 1.44 and 2.42. In which medium the speed of light is least ?

• A. water
• B. glass
• C. kerosene
• D. diamond

Hint:

Refractive index (\(n\)) tells you how much light slows down in a medium compared to vacuum. Formula: \(n = \frac{\text{Speed of light in vacuum (c)}}{\text{Speed of light in medium (v)}}\) or \(v = \frac{c}{n}\). This means:
{Higher} refractive index (\(n\)) \(\rightarrow\) {Lower} speed of light (\(v\)) in the medium.
{Lower} refractive index (\(n\)) \(\rightarrow\) {Higher} speed of light (\(v\)) in the medium. To find where speed is LEAST, look for the HIGHEST refractive index. Diamond (n=2.42) has the highest refractive index among the options, so light travels slowest in diamond.

Answer 1

The Correct Option is D

Concept: The refractive index (\(n\)) of a medium is related to the speed of light in vacuum (\(c\)) and the speed of light in that medium (\(v\)) by the formula: \[ n = \frac{c}{v} \] This can be rearranged to find the speed of light in the medium: \[ v = \frac{c}{n} \] From this relationship, we can see that the speed of light in a medium (\(v\)) is inversely proportional to its refractive index (\(n\)). This means:
The higher the refractive index of a medium, the lower the speed of light in that medium.
The lower the refractive index of a medium, the higher the speed of light in that medium. To find the medium in which the speed of light is least, we need to find the medium with the highest refractive index. Step 1: List the given refractive indices
Water: \(n_w = 1.33\)
Glass: \(n_g = 1.5\)
Kerosene: \(n_k = 1.44\)
Diamond: \(n_d = 2.42\) Step 2: Identify the medium with the highest refractive index Comparing the refractive indices: \(1.33<1.44<1.5<2.42\) The highest refractive index among the given substances is that of diamond (\(n_d = 2.42\)). Step 3: Determine the medium with the least speed of light Since the speed of light is inversely proportional to the refractive index, the medium with the highest refractive index will have the least speed of light. Diamond has the highest refractive index (2.42). Therefore, the speed of light will be least in diamond.