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

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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