Absolute refractive index of diamond is 2.4 find the speed of light in diamound if speed of light is 3 * 10 rais to power 8?

Question

Answer

We know formula

n = c/v

where

n = refractive index

C = speed of light in vacuum = 3 × 10^8

And

v = velocity of light in Given Medium ( here the medium is diamond )

So now putting n = 2.42 and c = 3 x 10^8 we have,

2.42 = 3×10^8/v

v = 3×10^8/2.428

v = 1.66 × 10^8 m/s approx

Answer

N=c/v 2.4= 3×10^8/ v v=1.66×10^8 m/s Therefore the speed of light in diamond is 1.66×10^8m/s

Answer

Understanding Refractive Index
The refractive index (n) of a material is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that material (v). The formula is:

n = c / v
Where:
- n = refractive index
- c = speed of light in vacuum (approximately $3 \times 10^8$ m/s)
- v = speed of light in the material

Finding the Speed of Light in Diamond
Given that the refractive index of diamond is 2.4, we can rearrange the formula to find the speed of light in diamond (v):

v = c / n
Now, substituting the values:
- c = $3 \times 10^8$ m/s
- n = 2.4

Calculating the Speed
Now, plug in the values:
- v = $ \frac{3 \times 10^8 \text{ m/s}}{2.4} $

Performing the Division
Calculating this gives:
- v = $1.25 \times 10^8$ m/s

Summary of Results
- The speed of light in diamond is approximately:
- v = 1.25 × 10⁸ m/s
This indicates that light travels significantly slower in diamond compared to its speed in a vacuum due to the material's higher refractive index. This slower speed is what contributes to diamond's brilliance and optical properties.

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