A ray of light enters from air to any medium having a refractive index of 2. Calculate the speed of light in that medium.
Understand the Problem
The question is asking for the calculation of the speed of light in a medium when the refractive index is given. It specifies the context of a ray of light entering a medium from air.
Answer
The speed of light in the medium is \( V = 1.5 \times 10^8 \) m/s.
Answer for screen readers
The speed of light in the medium is ( V = 1.5 \times 10^8 ) m/s.
Steps to Solve
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Understand the given information The speed of light in a vacuum ($c$) is given as $3 \times 10^8$ m/s. The refractive index ($n$) of the medium is given as 2.
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Use the formula for speed of light in a medium The speed of light in a medium ($V$) can be calculated using the formula: $$ n = \frac{c}{V} $$ Rearranging this formula to solve for $V$ gives: $$ V = \frac{c}{n} $$
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Substitute the known values Now substitute the values of $c$ and $n$ into the rearranged formula: $$ V = \frac{3 \times 10^8 \text{ m/s}}{2} $$
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Calculate the speed Now perform the division: $$ V = 1.5 \times 10^8 \text{ m/s} $$
The speed of light in the medium is ( V = 1.5 \times 10^8 ) m/s.
More Information
The speed of light varies in different media due to the medium's refractive index, which indicates how much light bends when entering the medium. In this case, a refractive index of 2 means that light travels half as fast in this medium compared to its speed in a vacuum.
Tips
- Confusing refractive index and speed: Remember that a higher refractive index means a lower speed of light in that medium.
- Arithmetic errors: Ensure that you double-check calculations, especially with scientific notation.
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