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.
