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Field of view of cylindrical mirrors

  1. Jun 6, 2006 #1
    Sir,
    A driving mirror consists of a cylindrical mirror of radius 10 cm and the length over the curved surface is 10 cm. If the of the driver be assumed to be at a great distance from the mirror, what is the field of view of the mirror in radian?
    I don’t have any idea about cylindrical mirrors. Could you please give a hint on how to solve this problem?
     
  2. jcsd
  3. Jun 9, 2006 #2
    I think this question could be expresses a little more clearly.

    We have a rear view mirror on a car. (This took me a while to figure out. I thought it was about some kind of optical resonator :rolleyes: ). The distance, measured horizontally ON the surface of the mirror is 10cm. If it formed a cylinder it would have a radius of 10cm. I person is standing 25 ft behind the car. They pull a laser pointer out of their pocket and shine it on the left edge of the rear view mirror. The light reflects at angle theta1. They then shine it on the right side of the mirror and the light reflects at an angle theta2. What is the difference between theta1 and theta2??
     
  4. Jun 9, 2006 #3
    Never mind that it is a cylindrical mirror. Treat each point on the edge of the mirror, where the light is reflected, as an individual plane mirror. Solve it using geometry (unless someone here can suggest a better method).
     
  5. Jun 9, 2006 #4
    Also, if the incoming beam is said to have an angle of zero radians, then

    |theta1-theta2| = |2 * theta1| = |2*theta2|
     
  6. Jun 10, 2006 #5

    Astronuc

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    Staff: Mentor

    A circular arc has length L = [itex]\theta[/itex] R, where [itex]\theta[/itex] is the angle subtending the arc and R is the radius.

    A full circle has circumference = 2[itex]\pi[/itex] R. The circumference is subtended by the angle 2[itex]\pi[/itex].
     
  7. Jun 12, 2006 #6
    Could you please explain in bit more detail?
     
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