A convex lens has a focal length of 0.33 m. The object distance is 0.7 m. What is the image distance?

Question

A convex lens has a focal length of 0.33 m. The object distance is 0.7 m. What is the image distance?

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Lệ Thu 4 years 2021-08-14T16:03:24+00:00 1 Answers 9 views 0

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  1. huyenthanh
    0
    2021-08-14T16:04:54+00:00
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    Answer:

    Explanation:

    1/v – 1/u = 1/f

    given, f = 0.3 m, u = -0.4m

    so, 1/v – 1/-0.4 = 1/0.3

    or, 1/v = 1/0.3 – 1/0.4 = 1/1.2

    v = 1.2 m

    now, differentiating 1/v – 1/u = 1/f with respect to t,

    -1/v² dv/dt + 1/u² du/dt = 0

    or, dv/dt = (v/u)² du/dt

    putting, du/dt = 0.01 m/s , v = 1.2 m and u = -0.4 m

    so, dv/dt = (1.2/-0.4)² × 0.01

    = 0.09 m/s

    hence, speed of image with respect to lens is 0.09 m/s .

    from formula of magnification

    magnification, m = v/u

    differentiating with respect to time both sides,

    dm/dt = (u dv/dt – vdu/dt)/u²

    = (-0.4 × 0.09 – 1.2 × 0.01)/(-0.4)²

    = (-0.036 – 0.012)/0.16

    = -0.048/0.16

    = -0.3 m/s

    hence, magnitude of rate of change of lateral magnification is 0.3 m/s

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