Question

A fish looking up through the water sees that the outside world is contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm beow the surface of the water, then the radius of the circle is i

Answer 1

Go through the upload, u will get r = 36/√7 cm

Answer 2

Answer:

Radius of the circle is r=0.136 m

Explanation:

The refractive index of the water is $\mu=\dfrac{3}{4}$

The depth of the fish under water is d=12 cm

The angle of incidence be i of the ray from the fish to the normal

We know that,

$\sin i=\dfrac{1}{\mu}$

From the triangular formula

$\tan i=\dfrac{1}{\sqrt{\mu^2-1}}$                             (1)

Let the radius of the circle is r

We know that

$\tan i=\dfrac{r}{h}$                            (2)

Equating equation 1 and 2 we get,

$\dfrac{1}{\sqrt{\mu^2-1}}=\dfrac{r}{h}\\r=\dfrac{h}{\sqrt{\mu^2-1}}\\r=\dfrac{0.12}{\sqrt{1.33^2-1}}\\r=0.136\ m$