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Calculate the refractive index of glass with respect to water given their refractive indices with respect to air.

Physics

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Answer

98\frac{9}{8}

Step-by-step solution

4 steps

  1. Identify the given refractive indices.

    The refractive index of water with respect to air (nwn_w) is 43\frac{4}{3}.
    The refractive index of glass with respect to air (ngn_g) is 32\frac{3}{2}.

  2. State the formula for the refractive index of glass with respect to water.

    The refractive index of glass with respect to water (ngwn_{gw}) is given by the ratio of the absolute refractive index of glass to the absolute refractive index of water:

    ngw=ngnwn_{gw} = \frac{n_g}{n_w}

  3. Substitute the given values into the formula.

    ngw=3243n_{gw} = \frac{\frac{3}{2}}{\frac{4}{3}}

  4. Simplify the expression to find the final answer.

    ngw=32×34n_{gw} = \frac{3}{2} \times \frac{3}{4} ngw=3×32×4n_{gw} = \frac{3 \times 3}{2 \times 4} ngw=98n_{gw} = \frac{9}{8}

    The refractive index of glass with respect to water is 98\frac{9}{8}.

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