2. Light enters from air into glass with a refractive index of 1.50. What is the speed of light in the glass? The speed of light in a vacuum is [tex]3 \times 10^8 \, \text{m} \, \text{s}^{-1}[/tex].



Answer :

To determine the speed of light in glass given the speed of light in a vacuum and the refractive index of the glass, we can use the relationship between these quantities. The refractive index ([tex]\(n\)[/tex]) is given by the formula:

[tex]\[ n = \frac{c}{v} \][/tex]

Where:
- [tex]\( n \)[/tex] is the refractive index,
- [tex]\( c \)[/tex] is the speed of light in a vacuum,
- [tex]\( v \)[/tex] is the speed of light in the medium (in this case, glass).

Given:
- The speed of light in a vacuum, [tex]\( c = 3 \times 10^8 \, \text{m/s} \)[/tex],
- The refractive index of glass, [tex]\( n = 1.50 \)[/tex].

We need to solve for [tex]\( v \)[/tex], the speed of light in glass. Rearranging the refractive index formula to isolate [tex]\( v \)[/tex]:

[tex]\[ v = \frac{c}{n} \][/tex]

Substitute the given values into the equation:

[tex]\[ v = \frac{3 \times 10^8 \, \text{m/s}}{1.50} \][/tex]

Now, divide [tex]\( 3 \times 10^8 \, \text{m/s} \)[/tex] by 1.50:

[tex]\[ v = 2 \times 10^8 \, \text{m/s} \][/tex]

Therefore, the speed of light in the glass is [tex]\( 2 \times 10^8 \, \text{m/s} \)[/tex] or 200,000,000 m/s.