Introduction:
When a ray of light enters a medium with a different refractive index, its speed changes. The refractive index is a measure of how much a medium can slow down light compared to a vacuum.

Given:
Refractive index of diamond = 2.42

Calculating the Speed of Light in Diamond:
The speed of light in a medium is given by the equation:

v = c/n

Where:
v = speed of light in the medium
c = speed of light in vacuum (approximately 3 × 10^8 m/s)
n = refractive index of the medium

To calculate the speed of light in diamond, we need to substitute the given values into the equation:

v = (3 × 10^8 m/s) / 2.42

Simplifying this equation:

v = 1.24 × 10^8 m/s

Thus, the speed of light in diamond is approximately 1.24 × 10^8 m/s.

Calculating the Percentage Reduction in Speed:
To calculate the percentage reduction in speed, we need to determine the difference between the speed of light in air and the speed of light in diamond, and then express it as a percentage of the initial speed of light in air.

The reduction in speed can be calculated as:

Reduction in speed = Speed of light in air - Speed of light in diamond

Substituting the values:

Reduction in speed = (3 × 10^8 m/s) - (1.24 × 10^8 m/s)

Simplifying this equation:

Reduction in speed = 1.76 × 10^8 m/s

To calculate the percentage reduction, we divide the reduction in speed by the initial speed of light in air and multiply by 100:

Percentage reduction = (Reduction in speed / Speed of light in air) × 100

Substituting the values:

Percentage reduction = (1.76 × 10^8 m/s / 3 × 10^8 m/s) × 100

Simplifying this equation:

Percentage reduction = 58.67%

Therefore, the speed of light is reduced by approximately 58.67% when it enters the diamond from air.