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Calculate the speed of light in water given the speed of light in air and the refractive index of water.

Physics

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Step-by-step solution

4 steps

  1. Identify the given values.

    The speed of light in air (cairc_{air}) is given as 3×108 m/s3 \times 10^8 \, \text{m/s}.
    The refractive index of light from air to water (nwatern_{water}) is given as 43\frac{4}{3}.

  2. Use the formula for refractive index.

    The refractive index (nn) of a medium is defined as the ratio of the speed of light in a vacuum (or air, as an approximation) to the speed of light in that medium (vv).

    n=cairvn = \frac{c_{air}}{v}

    In this case, we are looking for the speed of light in water (vwaterv_{water}), so the formula becomes:

    nwater=cairvwatern_{water} = \frac{c_{air}}{v_{water}}

  3. Rearrange the formula to solve for the speed of light in water.

    vwater=cairnwaterv_{water} = \frac{c_{air}}{n_{water}}

  4. Substitute the given values and calculate the speed of light in water.

    vwater=3×108 m/s43v_{water} = \frac{3 \times 10^8 \, \text{m/s}}{\frac{4}{3}} vwater=(3×108 m/s)×34v_{water} = (3 \times 10^8 \, \text{m/s}) \times \frac{3}{4} vwater=94×108 m/sv_{water} = \frac{9}{4} \times 10^8 \, \text{m/s} vwater=2.25×108 m/sv_{water} = 2.25 \times 10^8 \, \text{m/s}

    The correct value of the speed of light in water is \boxed{\text{2.25 \times 10^8 m/s}}.

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