What is the Critical Angle for Light Passing Through a Contaminated Lake?

[Winzer]

Homework Statement

A point source of light is located 3.56 m below the surface of a large lake of clear, but contaminated, water (Lake Ontario, where n = 1.28). Find the area of the largest circle on the lake's surface through which light coming from the source can emerge into the air.

Homework Equations

The Attempt at a Solution

Not sure where to start

 

[mgb_phys]

Lookup 'critical angle'

 

[Winzer]

ok:
$$sin(\theta)_c=\frac{n_air}{n_water}$$
$$\theta_c= 51.37$$
I use some trig to find the radius which is:
$$r=hcos(\theta_c)$$
And I can find the area from there, correct?

 

[mgb_phys]

Yes - but draw a sketch just to make sure you have the angle the right way round - it's always tricky when it's near 45deg.

 

[Winzer]

oops.
that $$r=hcos(\theta_c)$$ should be a $$r=htan(\theta_c)$$

 

[Winzer]

I get 90.48 m^2 but it is incorrect

 

[mgb_phys]

Theta is the angle between the ray that would just exit and the normal to the surface.
So by similair triangles it is also the internal angle between the ray and a line straight up from the surface to the source.

So the radius of the patch on the surface is tan(theta) * depth. The area is then of course pi r^2.

(I get 65.5m^2)

 

[Winzer]

Funny calc mistake,
but i got 62.36 m^2 and that is he correct answer

 

[mgb_phys]

oops - typed it out wrong! Always check your arithmatic!