Question

A type of glass block has a refractive index of 1.8.
(a) Calculate the speed of light in this glass. (Given speed of light in air \(c = 3 \times 10^8\) ms\(^{-1}\))
(b) If the width of this block is doubled, then what will be the speed of light in the block?

Hint:

The speed of light changes only when it enters a different medium. Within the same uniform medium, its speed is constant regardless of the path length.

Answer 1

Step 1: Understanding the Concept:
The refractive index (\( \mu \)) of a medium is defined as the ratio of the speed of light in vacuum (or air) to the speed of light in that medium.
Step 2: Key Formula or Approach:
\[ \mu = \frac{c}{v} \implies v = \frac{c}{\mu} \]
Step 3: Detailed Explanation:
Given:
Refractive index of glass (\( \mu \)) = 1.8
Speed of light in air (\( c \)) = \( 3 \times 10^{8} \text{ ms}^{-1} \)
Calculation:
\[ v = \frac{3 \times 10^{8}}{1.8} \]
\[ v = \frac{30}{18} \times 10^{8} \]
\[ v = \frac{5}{3} \times 10^{8} \]
\[ v \approx 1.666... \times 10^{8} \text{ ms}^{-1} \]
Rounding to two decimal places: \( v = 1.67 \times 10^{8} \text{ ms}^{-1} \).
Step 4: Final Answer:
The speed of light in the glass is \( 1.67 \times 10^{8} \text{ ms}^{-1} \).
(b)
Step 1: Understanding the Concept:
The speed of light in a medium is a characteristic property of the material of the medium and the wavelength of light used.
Step 2: Detailed Explanation:
The speed of light in a medium depends on its refractive index (\( v = c/\mu \)).
The refractive index depends on the nature of the material (optical density) and the frequency/wavelength of the light.
Changing the physical dimensions (width, height, or thickness) of the block does not change the material or the optical density.
Therefore, the refractive index remains 1.8, and the speed of light remains unchanged.
Step 3: Final Answer:
The speed of light in the block remains \( 1.67 \times 10^{8} \text{ ms}^{-1} \).