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Complete the table for question 8.(a)(ii), calculating sin I and sin r for the given angles.

Physics

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Here's the solution for question 8. (a) (ii):

To complete the table, we need to calculate the sine of the given angles of incidence (I) and refraction (R). We will use a calculator and round the values to three decimal places for consistency.

  1. Calculate the missing values for sin⁡I\sin I.

    • For I=30∘I = 30^\circ: sin⁡(30∘)=0.500\sin(30^\circ) = 0.500
    • For I=40∘I = 40^\circ: sin⁡(40∘)≈0.643\sin(40^\circ) \approx 0.643
    • For I=60∘I = 60^\circ: sin⁡(60∘)≈0.866\sin(60^\circ) \approx 0.866
    • For I=80∘I = 80^\circ: sin⁡(80∘)≈0.985\sin(80^\circ) \approx 0.985
  2. Calculate the missing values for sin⁡R\sin R.

    • For R=19∘R = 19^\circ: sin⁡(19∘)≈0.326\sin(19^\circ) \approx 0.326
    • For R=30∘R = 30^\circ: sin⁡(30∘)=0.500\sin(30^\circ) = 0.500
    • For R=35∘R = 35^\circ: sin⁡(35∘)≈0.574\sin(35^\circ) \approx 0.574
    • For R=41∘R = 41^\circ: sin⁡(41∘)≈0.656\sin(41^\circ) \approx 0.656

    The completed table is shown below:

    I203040506080R131925303541Sin I0.340.5000.6430.750.8660.985Sin r0.2220.3260.500.5000.5740.656\begin{array}{|c|c|c|c|c|c|c|} \hline \text{I} & 20 & 30 & 40 & 50 & 60 & 80 \\ \hline \text{R} & 13 & 19 & 25 & 30 & 35 & 41 \\ \hline \text{Sin I} & 0.34 & \textbf{0.500} & \textbf{0.643} & 0.75 & \textbf{0.866} & \textbf{0.985} \\ \hline \text{Sin r} & 0.222 & \textbf{0.326} & 0.50 & \textbf{0.500} & \textbf{0.574} & \textbf{0.656} \\ \hline \end{array}
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