What will be the time taken by light to travel 2cm thickness of glass of refractive index 1.5?
2.5×10−10s
Calculating Light Travel Time in Glass
Understanding how light travels through different materials requires knowing the speed of light in that material. This speed is related to the speed of light in a vacuum by the material's refractive index.
Given Information
- Thickness of glass (distance), \(d = 2\) cm
- Refractive index of glass, \(n = 1.5\)
Physics Principle: Speed of Light in a Medium
The speed of light in a medium (\(v\)) is slower than the speed of light in a vacuum (\(c\)). The relationship between them is given by the refractive index (\(n\)) of the medium:
\(n = \frac{c}{v}\)
From this, we can find the speed of light in the glass:
\(v = \frac{c}{n}\)
The speed of light in a vacuum is approximately \(c = 3 \times 10^8\) m/s.
Calculating Travel Time
We know that time taken (\(t\)) to travel a distance (\(d\)) at a constant speed (\(v\)) is given by:
\(t = \frac{d}{v}\)
Substitute the expression for \(v\) from the refractive index relationship into the time equation:
\(t = \frac{d}{\left(\frac{c}{n}\right)}\)
\(t = \frac{d \times n}{c}\)
Performing the Calculation
First, convert the thickness from centimeters to meters:
\(d = 2 \text{ cm} = 2 \times 10^{-2} \text{ m}\)
Now, plug the values into the formula \(t = \frac{d \times n}{c}\):
\(t = \frac{(2 \times 10^{-2} \text{ m}) \times 1.5}{3 \times 10^8 \text{ m/s}}\)
\(t = \frac{3 \times 10^{-2} \text{ m}}{3 \times 10^8 \text{ m/s}}\)
Simplify the expression:
\(t = \left(\frac{3}{3}\right) \times 10^{-2 - 8} \text{ s}\)
\(t = 1 \times 10^{-10} \text{ s}\)
Result
The time taken by light to travel 2 cm thickness of glass with a refractive index of 1.5 is \(1 \times 10^{-10}\) seconds.
Revision Table: Light Travel Time Calculations
| Concept | Formula | Notes |
|---|---|---|
| Speed of light in vacuum | \(c \approx 3 \times 10^8\) m/s | Constant reference speed |
| Refractive Index | \(n = \frac{c}{v}\) | Ratio of speed in vacuum to speed in medium |
| Speed in Medium | \(v = \frac{c}{n}\) | Derived from refractive index definition |
| Time, Distance, Speed | \(t = \frac{d}{v}\) | Basic kinematic relation |
| Time in Medium (combined) | \(t = \frac{d \times n}{c}\) | Useful direct formula |
Additional Information: Refractive Index and Light Speed
The refractive index is a dimensionless quantity that tells us how much the speed of light is reduced when it passes through a medium compared to its speed in a vacuum. A higher refractive index means light travels slower in that medium.
- Vacuum has a refractive index of exactly 1, meaning light travels at its maximum speed (\(c\)).
- Air has a refractive index very close to 1 (around 1.0003), so light speed in air is almost the same as in a vacuum.
- Water has a refractive index of about 1.33.
- Typical glass has a refractive index ranging from about 1.5 to 1.7.
- Diamond has a very high refractive index, around 2.42, which contributes to its sparkle because light slows down significantly and bends more sharply.
This change in speed is also responsible for the phenomenon of refraction, where light bends as it crosses the boundary between two different media.
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