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A light ray travels from oil (n=2) into glass (n=1.5). If the angle of incidence is 30 degrees, what is the angle of refraction?

Physics

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Answer

r≈41.81∘r \approx 41.81^\circ

Step-by-step solution

5 steps

  1. Identify the given values.

    The light ray is incident from Oil into Glass.
    The refractive index of Oil is noil=63=2n_{oil} = \frac{6}{3} = 2.
    The refractive index of Glass is nglass=32=1.5n_{glass} = \frac{3}{2} = 1.5.
    The angle of incidence in Oil is θoil=30∘\theta_{oil} = 30^\circ.
    The angle of refraction in Glass is rr.

  2. Apply Snell's Law.

    Snell's Law states n1sin⁡θ1=n2sin⁡θ2n_1 \sin \theta_1 = n_2 \sin \theta_2.
    In this case, noilsin⁡θoil=nglasssin⁡rn_{oil} \sin \theta_{oil} = n_{glass} \sin r.

  3. Substitute the values into Snell's Law.

    2×sin⁡30∘=1.5×sin⁡r2 \times \sin 30^\circ = 1.5 \times \sin r

  4. Solve for sin⁡r\sin r.

    We know that sin⁡30∘=0.5\sin 30^\circ = 0.5.

    2×0.5=1.5×sin⁡r2 \times 0.5 = 1.5 \times \sin r 1=1.5×sin⁡r1 = 1.5 \times \sin r sin⁡r=11.5\sin r = \frac{1}{1.5} sin⁡r=132\sin r = \frac{1}{\frac{3}{2}} sin⁡r=23\sin r = \frac{2}{3}

  5. Calculate the angle rr.

    r=arcsin⁡(23)r = \arcsin\left(\frac{2}{3}\right) r≈41.81∘r \approx 41.81^\circ

    The value of rr is approximately 41.81∘41.81^\circ.

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