Flashlight 65 degrees conics question whats produced?

[aisha]

A flash light is pointed at a wall so that the angle between the beam and the wall is 65 degrees

a) which conic section is produced? I am not sure if this is asking for the shape but I think the answer is an ellipse

b) How would you adjuct the angle of the beam to produce a circle on the wall? I think if the angle between the beam and the wall is 180 degrees than a circle will be produced on the wall

Can someone please help me out?

 

[HallsofIvy]

I have a problem with part a): the answer will depend upon "angle of divergence" of the flashlight itself. If that angle is very small (like a cylindrical beam), yes, almost any angle will give an ellipse. On the other hand, if the angle of divergence large (close to 180 degrees), almost any angle will give a parabola or hyperbola.

For part b) where exactly are you measuring the angle? Of course, to get a circle, you aim the flash light directly at the wall. The angle the beam makes with the wall is 90 degrees, not 180 degrees.

 

[aisha]

I don't think part a is that complicated I think its the most obvious answer, if I ask my teacher the angle of divergence she will think I am tryin to be OVER smart lol and am missing the obvious.

 

[HallsofIvy]

Are you saying that you KNOW the answer? What exactly do you believe is "the most obvious answer"? An ellipse?

Why do you have such a low opinion of your teacher?

 

[aisha]

We haven't talked about angle of divergence in this unit that's why I think it can't be that complicated.

I think the answer may be an ellipse but I am not sure. If you weren't to think about the angle of divergence what would u say?

 

[HallsofIvy]

A conic section is a parabola if one side of the cone is parallel to the wall, a hyperbola if that side goes AWAY from the wall, If, for example, the angle at the vertex of the cone (the angle of divergence) is 45 degrees, then with the axis of the cone (the direction you are aiming the flashlight) at 45 degrees, the conic section is a parabola. If the angle you are aiming the flash light is 65 degress, like in this problem, yes, you get an ellipse. You would get a parabola only if the angle of divergence of the light beam is 65 degrees, a hyperbola if it is larger than 65 degrees. Those are unlikely angles for a flashlight so, yes, you are probably right that the figure would be an ellipse- but it's worth asking your teacher about. All teachers I know welcome questions about possible variations of problems