Question

What does \[\frac{\sin i}{\sin r}\] equal in terms of the speeds in the two media?

Options

• \[\frac{v_1}{v_2}\]

• \[v_1v_2\]

• \[\frac{v_1}{v_1+v_2}\]

• \[\frac{v_2}{v_1}\]

Answer 1

Substitute \[BC=v_1\tau\] and \[AE=v_2\tau\] into \[\frac{\sin i}{\sin r}=\frac{BC}{AE}\]. Cancelling the common time \[\tau\] gives \[\frac{\sin i}{\sin r}=\frac{v_1}{v_2}\].