A reflecting telescope contains a mirror shaped like a paraboloid of revolution. If the mirror is 4 inches across at its opening and is 3 inches deep, where will the collected light be concentrated?
Well, well, well, we've got ourselves a mirror question! Time to reflect on this one. So, we have a paraboloid of revolution mirror that's 4 inches across at its opening and 3 inches deep. Now, where will all that collected light be concentrated?
Hmm, I don't know about you, but I'm imagining a bunch of mischievous photons getting together for a little party inside that mirror. And when they all bounce around and have a jolly old time, they're going to be concentrated at a special place.
And that special place, my friend, is called the focal point! You see, the unique shape of the paraboloid mirror causes all those light rays to converge at the focal point. It's like the party hotspot of the telescope!
So, in this case, the collected light will be concentrated at the focal point of the mirror. And where exactly is that? Well, I'd say grab a measuring tape or a ruler and measure 3 inches from the center of the mirror opening towards the back. That's where you'll find the focal point, and where all the light will gather for a good old photon powwow!
Remember, it's all about that funky paraboloid shape that does the trick. Now go and enjoy some stargazing with your concentrated light!
To determine where the collected light will be concentrated in a reflecting telescope, we need to consider the shape of the mirror and the focal point.
In a reflecting telescope, the mirror is shaped like a paraboloid of revolution. This means that its cross-sectional shape is like a parabola rotated around its axis.
Given that the mirror is 4 inches across at its opening and 3 inches deep, we can assume that the mirror has a symmetrical shape.
The focal point, also known as the focus, of a paraboloid mirror is located at a distance equal to half its depth (or twice its focal length) from the vertex of the mirror.
In this case, the depth of the mirror is 3 inches, so the focal point will be located at a distance of 3/2 = 1.5 inches from the vertex of the mirror.
Therefore, the collected light will be concentrated at a point located 1.5 inches from the vertex of the mirror.
To determine where the collected light will be concentrated in a reflecting telescope with a mirror shaped like a paraboloid of revolution, we need to use the property that light reflecting off a parabolic surface converges at the focus.
Given that the mirror is shaped like a paraboloid of revolution, we can assume it has a symmetrical shape. The diameter of the mirror, or the opening, is given as 4 inches. From this, we can deduce that the distance from the center of the mirror to its opening is 2 inches.
The depth of the mirror is given as 3 inches. The distance from the center of the mirror to the deepest point of the parabolic shape is half of this depth, which is 1.5 inches.
Since the mirror is symmetrical, the focus of light will be at a distance equal to the depth of the mirror measured along its axis of symmetry. In this case, the focus will be 1.5 inches away from the center of the mirror.
Therefore, the collected light will be concentrated at a point 1.5 inches away from the center of the mirror.