First slide

Total internal reflection - Ray optics and optical instruments

Question

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is 12 cm below the surface, the radius of this circle in cm is

Moderate

A

$36 \sqrt{5}$
B

$4 \sqrt{5}$
C

$36 \sqrt{7}$
D

$\frac{36}{\sqrt{7}}$

Solution

$\sin c = \frac{1}{μ} = \frac{r}{\sqrt{r^{2} + h^{2}}} r = \frac{3 h}{\sqrt{7}} = \frac{3 \times 12}{\sqrt{7}} = \frac{36}{\sqrt{7}}$

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