Question

A point source of light is 80.0 cm below the surface of

a body of water. Find the diameter of the circle at the surface

through which light emerges from the water.

Answer 1

The diameter of the circle at the surface is 1.814 m.

Step-by-step explanation:

Given that,

Depth = 80 cm

Let the critical angle be c.

From Snell's law

`sin c=(1)/(n)`

`c=sin^(-1)(1)/(n)`

The value of n for water,

`n = (4)/(3)`

Put the value of n in the equation (I)

`c =sin^(-1)(3)/(4)`

`c=48.6^(\circ)`

We know that,

`tan c=(r)/(h)`

We calculate the radius of the circle

`r =h tan c`

`r=80*10^(-2)*\tan48.6^(\circ)`

`r =0.907\ m`

The diameter of the circle at the surface

`d =2* r`

`d =2* 0.907`

`d =1.814\ m`

Hence, The diameter of the circle at the surface is 1.814 m.