Please help with refraction problem (algebra-based physics)

  • Thread starter Thread starter mirracle4
  • Start date Start date
  • Tags Tags
    Physics Refraction
AI Thread Summary
A user encountered a problem calculating the angle of a light ray emerging from a swimming pool using Snell's Law. They initially calculated the angle of incidence as 61.2 degrees but received a "domain error" when attempting to find the angle of refraction. The error was due to using the angle measured from the water surface instead of the normal to the surface. After clarification, the user corrected their approach and successfully solved the problem. The discussion highlighted common pitfalls in applying Snell's Law, including the potential for total internal reflection.
mirracle4
Messages
3
Reaction score
0
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!
 
Physics news on Phys.org
mirracle4 said:
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?
 
Last edited:
SammyS said:
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.
 
mirracle4 said:
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.
 
Last edited:
SammyS said:
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 :smile:
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top