Imagine that you are standing a distance x away from a wall, and a plane mirror is hanging on the wall. the top of the mirror is at the same height as the top of your head.
How long does the mirror have to be in order that you can see your feet?
Does the answer depend on the distance x?
You only need one that goes to half the distance between your eyes and the floor in order to see all of yourself in it.
The reflected light from your feet has to travel halfway up the distance between your eyes and your feet in order to strike the mirror at the right angle to get reflected to your eyes. Remember the angle in insidence is the angle of reflection.
It does not matter how close you are to the mirror; you will still need only the same length mirror 1/2 the distance to the floor. the angle to that half way point changes by the same amount for the light from your feet and teh mirror reflection to your eyes. You'll be looking at teh point halfway to the floor to see your feet.
A Mirror that is below that level will only show you more of the the floor in front of your feet.
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High Quality Content by WIKIPEDIA articles Xray optics is the branch of optics which manipulates Xrays instead of visible light. While lenses for visible light are made of a transparent material with an index of refraction substantially different from 1, there is no equivalent material for Xrays. The only methods of Xray manipulation, other than simple image modulation, are through reflection, diffraction and interference effects, or by combining a number of lenses into a compound refractive lens. The basic idea is to reflect a beam of Xrays from a surface and to measure the intensity of Xrays reflected in the specular direction (reflected angle equal to incident angle). It has been shown that a reflection off a parabolic mirror followed by a reflection off a hyperbolic mirror can lead to the focusing of Xrays. Author: Surhone, Lambert M./ Timpledon, Miriam T./ Marseken, Susan F. Binding Type: Paperback Number of Pages: 104 Publication Date: 2010/07/01 Language: English Dimensions: 5.98 x 9.01 x 0.24 inches
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Optics gives a comprehensive and balanced account of traditional optics as well as some of the recent developments in this field while meeting the requirements of a course on optics meant for undergraduate students of science and engineering.
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Remix #5: BBC2 Mirror vs Optics
Physics Problem(The Nature of Light and the laws of geometric Optics)?
The problem states...
The distance of a lightbulb from a large plane mirror is five times the distance of a person from the plane mirror. Light from the bulb reaches the person by two paths. It travels to the mirror at an angle of incidence , and reflects from the mirror to the person. It also travels directly to the person without reflecting off the mirror. The total distance traveled by the light in the first case is twice the distance traveled by the light in the second case. Find the value of the angle .
Let x be the distance from the light to the wall on which the mirror is mounted. Then the distance from the person to the wall is 5x. Also let y be the component of distance parallel to the wall from the light to the point on the mirror that the light reaches before hitting the person. The light bulb is therefore be located at (x, y) with respect to this point and the person at (5x, -5y).
Let θ be the angle with respect to the normal at which the light strikes the mirror and reflects to the person. Then
tan θ = y/x. The total distance traveled by the reflected ray is therefore
√(x² + y²) for the incident ray and
√((5x)² + (-5y)²) or 5√(x² + y²) for the reflected ray, for a total distance of
6√(x² + y²)
The direct ray to the prson would be a distance of
√[(5x−x)² + (-5y−y)²]
= √(16x² + 36y²)
= √(16x² + 16y² + 20y²)
= 4√(x² + y² + 5/4y²)
The problem gives us the fact that the total distance for the reflected ray is twice that for the direct ray, which means
6√(x² + y²) = 2[4√(x² + y² + 5/4y²)]
= 8√(x² + y² + 5/4y²)
If we square both sides to remove the radicals and divide through by x², we get
36(1 + tan² θ) = 64(1 + tan² θ) + 80 tan² θ
to give
tan² θ = -7/36
an impossible number for any real angle. The conditions are therefore inconsistent as stated.
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