Question

Anyone able to help with this?

Answer 1

$W = 23.7°$

Step-by-step explanation:

The formula given is the statement of Snell's law of refraction. We are given the following:

$I_a = 1.0003$

$I_w = 1.3$

$A = 31.5°$

So we need to find the angle of refraction W. Starting with Snell's law,

$\dfrac{I_w}{I_a} = \dfrac{\sin A}{\sin W} \Rightarrow \sin W = \left(\dfrac{I_a}{I_w}\right)\sin A$

Plugging in the given values, we get

$\sin W = \left(\dfrac{1.0003}{1.3}\right)\sin{31.5°} = 0.402$

Solving for the angle W, we then get

$W = \sin^{-1}(0.402) = 23.7°$