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Simple lens question (camera)

  • 21-05-2010 2:36pm
    #1
    Smythe
    Registered Users, Registered Users 2 Posts: 434 ✭✭


    Was wondering if someone could help...
    A simple camera has a converging lens of focal length 50.0 mm.

    It is used to photograph a tree 3.00 m high.

    The tree is 8.00 m away from the lens.

    Calculate the distance v between the lens and the film, giving your answer in mm to three significant figures.

    Using:
    1/f = 1/u + 1/v

    1/50 = 1/8000 + 1/(v)
    v = 50.3 mm


    Then to calculate the linear magnification of the image, using m = v/u with same v and u values from above? (both in metres)

    i.e.

    m = 0.0503 / 8 = 0.0063

    Though as the image gets flipped upside down it's probably:
    m = -0.0503 / 8 = -0.0063


    Thank you :)


Comments

  • #2
    Delphi91
    Registered Users, Registered Users 2 Posts: 1,501 ✭✭✭Delphi91


    Smythe wrote: »
    ...Then to calculate the linear magnification of the image, using m = v/u with same v and u values from above? (both in metres)

    i.e.

    m = 0.0503 / 8 = 0.0063

    Though as the image gets flipped upside down it's probably:
    m = -0.0503 / 8 = -0.0063


    Thank you :)

    You were doing fine up to here. To all intents and purposes the object as at infinity compared to the focal length of the lens, therefore the image should be formed at the focal point - focal length is 50mm, image distance is 50.3mm.

    As for the magnification question, yes m=v/u with an answer of (+)0.0063. The positive value indicates that the image is inverted (despite what you might think) and the 0.0063 indicates that the image is vastly smaller than the object (it's approxomately 1.9cm high - 300 * 0.0063)


  • #3
    Smythe
    Registered Users, Registered Users 2 Posts: 434 ✭✭Smythe


    Thanks very much Delphi91.

    So, m = v/u is the correct equation for linear magnification?

    I wasn't sure as I was told that the correct equation for magnification has the minus sign, making it:
    m = -v/u
    Which left me quite confused...


  • #4
    Delphi91
    Registered Users, Registered Users 2 Posts: 1,501 ✭✭✭Delphi91


    Smythe wrote: »
    Thanks very much Delphi91.

    So, m = v/u is the correct equation for linear magnification?

    I wasn't sure as I was told that the correct equation for magnification has the minus sign, making it:
    m = -v/u
    Which left me quite confused...

    Well, I always keep it as m = v/u and adjust the sign of v depending on whether the image (and therefore the image distance) is virtual or not. The only time this will happen (for a converging lens) is if the object is inside the focal point (i.e. u < f).

    If that is the case, you get a negative answer for v and also for m which implies an erect image - try it with a magnifying glass, the only time you get a magnified image is when the object is inside the focal point.


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