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What is the refractive index in a medium...

What is the refractive index in a medium where the speed of light is `1.5xx10^8` m/s ?

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To find the refractive index of a medium where the speed of light is given, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Speed of Light in Air**: The speed of light in air (or vacuum) is approximately \( c = 3 \times 10^8 \) m/s. 2. **Identify the Speed of Light in the Medium**: The speed of light in the given medium is provided as \( v = 1.5 \times 10^8 \) m/s. 3. **Use the Formula for Refractive Index**: The refractive index \( n \) of a medium is calculated using the formula: \[ n = \frac{c}{v} \] where \( c \) is the speed of light in air and \( v \) is the speed of light in the medium. 4. **Substitute the Values**: Substitute the known values into the formula: \[ n = \frac{3 \times 10^8 \text{ m/s}}{1.5 \times 10^8 \text{ m/s}} \] 5. **Perform the Calculation**: Simplifying the fraction: \[ n = \frac{3}{1.5} = 2 \] 6. **Conclusion**: The refractive index of the medium is \( n = 2 \). ### Final Answer: The refractive index of the medium is **2**. ---
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