Answer to Question #228774 in Electricity and Magnetism for Arvin Shopon

Question

a) Jessica examined the reflections visible from the water surface of the aquarium. At what angle does the light from the lamp have to hit the surface of the water for the light to be completely polarized?

b) Jessica continued her research by dropping a glass cube on the bottom of the aquarium. At what angle does the light have to hit the surface of the glass cube in order for the goldfish swimming in the aquarium to see the light reflected from it perfectly polarized?

Answer 1

We know that

(A)Snell's law

$n_{a}sin\theta_{a}=n_{w}sin\theta_{w}$

$n_a=1\\n_w=1.33\\n_g=1.5$

Put value

$1\times sin60°=1.33\times sin\theta_{w}$

$sin\theta=\frac{sin60°}{1.33}\\\theta_{w}=sin^{-1}(0.6511)=40.62°$

(b)

$n_{w}sin\theta_{w}=n_{g}sin\theta_{g}$

$1.33\times sin40.62°=1.5\times sin\theta_{w}$

$$sin\theta=\frac{1.33\times sin40.62°}{1.5}\\\theta_{w}=sin^{-1}(0.5772)=35.25°$$