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Homework Help: Optics spherical mirror

  1. Feb 18, 2006 #1
    Hi,

    Doing an optics course I'm getting a bit confused about sign the conventions at time, can somebody check my answers here?

    A spherical concave mirror of radius, R= 100mm has a real object placed at an axial distance So from its vertex.

    Q1 Obtain the focal length of the mirror

    1/ f = -2/R => f = -R/2 = -(-100mm)/2 = 50 mm right?

    Q2 If an object is placed at a distance (i) Object distance, So = 200mm and then (ii) So = 20mm find the image positions, whether they are real or virtual and there magnifications.

    (i) 1/Si = 1/f - 1/So = 1/50 - 1/200 = 150/10000 mm^-1. Si = image distance
    M = -Si/So = -(10000/150 mm) / (200 mm) = -1/3

    So the image is real, 67mm to the right of the mirror and is inverted and minified by a factor of 1/3.


    (ii) 1/Si = 1/f - 1/So = 1/50 - 1/20 = - 30/1000 mm^-1
    M = -Si/So = -(-1000/30 mm) / (20 mm) = 5/3

    So the image is virtual, 33mm to the left of the mirror and is erect and magnified by a factor of 5/3.
     
    Last edited: Feb 18, 2006
  2. jcsd
  3. Feb 18, 2006 #2
    Also.
    An object is placed 5 cm from a thin equi-convex lens of focal length 4cm. Another thin equi-convex lens is placed on the same axis as the first and 9cm away from it, on the side further from the object. It has a focal length of 5cm.

    (i) Find the position of the image. Is the image real

    A: The image will be formed 3.475 cm to the right of lens 2 (therefore it's real ), or 17.475cm to the right of the object.

    (ii) What are the magnifications of the intermediate and final image.

    A: M(int) = -Si1/So1 = -(20cm)/(5cm) = -4
    M(2) = -(Si2)/(So2) = -(55/16)/(-11) = 0.3125
    M(tot) = M(int).M(2) = -1.25

    Would appreciate somebody telling me it's all correct as well as pointing out any mistakes.
     
  4. Feb 19, 2006 #3
    Bump. I take it nobody does optics then.
     
  5. Feb 19, 2006 #4

    nrqed

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    This looks right to me. the signs are ok. A quick check with a ray diagram agrees qualitatively with your results too. (it`s useful to know how to draw ray diagrams to check results like this).

    Pat
     
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