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The speed of light in a vacuum is approximately [tex]2.99 \times 10^8 \, \text{m/s}[/tex], and the speed of light through a piece of glass is approximately [tex]1.97 \times 10^8 \, \text{m/s}[/tex].

What is the index of refraction for the piece of glass?

A. 0.66
B. 1.52
C. [tex]1.02 \times 10^8[/tex]
D. [tex]4.96 \times 10^8[/tex]

Sagot :

GinnyAnsweridn
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].
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