A diverging lens of focal length 18.0m is used to view a shark that is 90.0m away from the lens. If the image formed is 1.0m long, calculate

Question

A diverging lens of focal length 18.0m is used to view a shark that is 90.0m away from the lens. If the image formed is 1.0m long, calculate the: (i) image distance; (ii) length of the shark.

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Neala 4 years 2021-08-22T17:28:29+00:00 1 Answers 8 views 0

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  1. Tryphena
    0
    2021-08-22T17:29:36+00:00
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    Answer:

    i. + 22.5 m ii. 4.0 m

    Explanation:

    i. Image distance

    Using the lens formula

    1/u + 1/v = 1/f where f = focal length = + 18.0 m, u = object distance = distance of shark away from lens = + 90.0 m and v = image distance from lens = unknown

    So, we find v

    1/v = 1/f – 1/u

    = 1/+18 – 1/+90

    = (5 – 1)/90

    = 4/90

    v = 90/4

    = + 22.5 m

    So the image is real and formed 22.5 m away on the other side of the lens.

    ii Length of Shark

    Using the magnification formula, m = image height/object height = image distance/object distance. image height = 1.0 m where object height = length of shark.

    m = image distance/object distance

    = v/u

    = +22.5/+90

    = 0.25

    0.25 = image height/object height

    So,

    object height = image height/0.25

    = 1.0 m/0.25

    = 4.0 m

    So, the length of the shark is 4.0 m

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