Question

The refractive index of glass is 1.6 and the speed of light in glass will be ……… . The speed of light in vacuum is \( 3.0 \times 10^8 \) ms\(^{-1}\).

Hint:

The speed of light in a medium is always less than the speed of light in a vacuum. It is given by \( v = \frac{c}{n} \), where \( n \) is the refractive index.

Answer 1

Step 1: Understanding the Relationship Between Speed of Light and Refractive Index 
The speed of light in a medium (\( v \)) is related to the refractive index (\( n \)) of the medium by: \[ v = \frac{c}{n} \] where:
- \( c = 3.0 \times 10^8 \) m/s (speed of light in vacuum),
- \( n = 1.6 \) (refractive index of glass). 
Step 2: Substituting the Given Values 
\[ v = \frac{3.0 \times 10^8}{1.6} \] \[ v = 1.875 \times 10^8 { m/s} \] 
Step 3: Rounding Off the Answer 
Approximating to three significant figures: \[ v \approx 1.88 \times 10^8 { m/s} \] 
Step 4: Conclusion 
Thus, the speed of light in glass is \( 1.88 \times 10^8 \) m/s.