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

(a) Calculation of speed of light in glass:
Step 1: Formula for Refractive Index
The refractive index (\(n\)) of a medium is the ratio of the speed of light in a vacuum/air (\(c\)) to the speed of light in the medium (\(v\)). \[ n = \frac{c}{v} \] Step 2: Given values
- Refractive index of glass, \(n = 1.8\)
- Speed of light in air, \(c = 3 \times 10^8\) m/s
Step 3: Calculation
Rearranging the formula to find the speed of light in glass (\(v\)): \[ v = \frac{c}{n} = \frac{3 \times 10^8}{1.8} \] \[ v = \frac{30}{18} \times 10^8 = \frac{5}{3} \times 10^8 \approx 1.67 \times 10^8 \text{ m/s} \] The speed of light in the glass is \(1.67 \times 10^8\) m/s.
(b) Effect of doubling the width:
The speed of light in a medium is an intrinsic property of that medium. It depends only on the optical density of the material, not on its physical dimensions like width, length, or thickness. Therefore, if the width of the block is doubled, the speed of light inside the block will remain the same (\(1.67 \times 10^8\) m/s).