A 4 mm object is observed by a magnifying lens as 1.25 cm. Calculate the ratio do/di.

Question

A 4 mm object is observed by a magnifying lens as 1.25 cm. Calculate the ratio do/di.

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Thu Thảo 3 years 2021-07-22T03:59:16+00:00 1 Answers 2 views 0

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  1. thuthuy
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    2021-07-22T04:00:48+00:00
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    Answer:

    dₒ/dᵢ = 0.32

    Explanation:

    From the question given above, the following data were obtained:

    Object height (Hₒ) = 4 mm

    Image height (Hᵢ) = 1.25 cm

    Ratio of object distance (dₒ) to image distance (dᵢ) [dₒ/dᵢ] =?

    Next, we shall convert 4 mm to cm. This can be obtained as follow:

    10 mm = 1 cm

    Therefore,

    4 mm = 4 mm × 1 cm / 10 mm

    4 mm = 0.4 cm

    Next, we shall determine the magnification of the lens. This can be obtained as follow:

    Object height (Hₒ) = 4 mm

    Image height (Hᵢ) = 1.25 cm

    Magnification (M ) =?

    M = Hᵢ/Hₒ

    M = 1.25 / 0.4

    M = 3.125

    Finally, we shall determine the ratio of object distance (dₒ) to image distance (dᵢ). This can be obtained as follow:

    Magnification (M) = 3.125

    Ratio of object distance (dₒ) to image distance (dᵢ) [dₒ/dᵢ] =?

    Magnification (M) = image distance (dᵢ) / object distance (dₒ)

    M = dᵢ/dₒ

    Invert

    1/M = dₒ/dᵢ

    1/3.125 = dₒ/dᵢ

    dₒ/dᵢ = 0.32

    Therefore, the ratio of object distance (dₒ) to image distance (dᵢ) [dₒ/dᵢ] is 0.32

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