The absolute refractive index of glass and water is 3/2 and 4/3, respectively. If the speed of light in glass is 2 × 10⁸, calculate the speed of light in:

• a) vacuum
• b) water

To find the speed of light in vacuum and water, we can use the relationship between the refractive index and the speed of light. The refractive index (n) is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v):

Speed of Light in Vacuum

The refractive index of glass is given as 3/2. Using the formula:

n = c / v

We can rearrange it to find the speed of light in vacuum:

c = n × v

Substituting the values for glass:

c = (3/2) × (2 × 10⁸)

Calculating this gives:

c = 3 × 10⁸ m/s

Speed of Light in Water

Next, we need to find the speed of light in water, where the refractive index is 4/3. Using the same formula:

v = c / n

Substituting the values:

v = (3 × 10⁸) / (4/3)

This simplifies to:

v = (3 × 10⁸) × (3/4)

Calculating this gives:

v = 2.25 × 10⁸ m/s

Summary of Results

• Speed of light in vacuum: 3 × 10⁸ m/s
• Speed of light in water: 2.25 × 10⁸ m/s