1. Apr 16, 2015

mirracle4

A flashlight on the bottom of a 4.10 m deep swimming pool sends a ray upward and at an angle so that the ray strikes the surface of the water 2.25 m from the point directly above the flashlight. What angle (in air) does the emerging ray make with the water's surface?

I attempted to find the angle of incidence by using the lengths given and the arc tangent function and then to plug it into Snell's Law (n1sinθ1 = n2sinθ2).

For the angle, I got 61.2 degrees by doing "inverse tan(4.10/2.25)." However, when solving Snell's Law for θ2 and plugging in all of the values, the calculator keeps saying "domain error." I'm plugging in... "inverse sin((n1sin61.2)/1.00) and I keep getting the error message. Please help!

2. Apr 16, 2015

SammyS

Staff Emeritus
Hello mirracle4. Welcome to PF !

Domain error, no doubt, results from you asking the calculator to find the arcsine of something greater than 1.

Is angle of incidence measured from the surface, or from the normal to the surface?

Last edited: Apr 17, 2015
3. Apr 17, 2015

mirracle4

Thanks SammyS! I got it right this time. I should have known that the angle I was using was the angle measured from the surface rather than the normal but somehow it slipped my mind.

4. Apr 17, 2015

SammyS

Staff Emeritus
It's good that you got it right now.

It's a mistake that I think we all have made some time or other. By the way, if in the future you have that domain error with Snell's Law, but you have done everything correctly, it's likely that it's a situation involving total internal reflection.

Last edited: Apr 17, 2015
5. Apr 18, 2015

Good to know