The image shows a calculation to determine the speed of light in a medium based on its refractive index.

Formula:

The speed of light in a medium $v$ is related to the speed of light in free space $c$ and the refractive index $n$ of the medium by the equation: $v = \frac{c}{n}$

In the image:

• The speed of light in free space $c$ is $3 \times 10^8 \ \text{m/s}$.
• The refractive index of the core $n$ is 1.5.

So, the speed of light in the core (or the medium) is calculated as: $v = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \ \text{m/s}$

Conclusion:

The speed of light in the core is $2 \times 10^8 \ \text{m/s}$.

Would you like more details on refractive index, or any further clarification?

Here are 5 related questions for further understanding:

1. What is the physical significance of refractive index in materials?
2. How does the speed of light change when moving from one medium to another?
3. What factors can affect the refractive index of a material?
4. Can the refractive index of a material be less than 1? Why or why not?
5. How is the refractive index measured experimentally?

Tip: In optical fibers, the refractive index of the core material plays a critical role in determining how light propagates through the fiber.