To find the index of refraction for the piece of glass, we use the formula for the index of refraction [tex]\( n \)[/tex], which is given by
[tex]\[ n = \frac{c}{v} \][/tex]
where:
- [tex]\( c \)[/tex] is the speed of light in a vacuum ([tex]\(2.99 \times 10^8 \, \text{m/s}\)[/tex]),
- [tex]\( v \)[/tex] is the speed of light in the medium (glass, in this case, [tex]\(1.97 \times 10^8 \, \text{m/s}\)[/tex]).
Let's calculate the index of refraction step by step:
1. Identify the given values:
- Speed of light in vacuum, [tex]\( c = 2.99 \times 10^8 \, \text{m/s} \)[/tex]
- Speed of light in glass, [tex]\( v = 1.97 \times 10^8 \, \text{m/s} \)[/tex]
2. Substitute these values into the formula:
[tex]\[ n = \frac{2.99 \times 10^8 \, \text{m/s}}{1.97 \times 10^8 \, \text{m/s}} \][/tex]
3. Simplify the expression by dividing the two numbers:
[tex]\[ n \approx 1.52 \][/tex]
Thus, the index of refraction for the piece of glass is approximately [tex]\( 1.52 \)[/tex].
Among the provided options:
- 0.66
- 1.52
- [tex]\(1.02 \times 10^8\)[/tex]
- [tex]\(4.96 \times 10^8\)[/tex]
The correct answer is [tex]\( 1.52 \)[/tex].
