Please help with refraction problem (algebra-based physics)

[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!

 

[SammyS]

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!

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?

 

[mirracle4]

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 measure from the surface, or from the normal to the surface?

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.

 

[SammyS]

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.

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.

 

[mirracle4]

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.

Good to know