Answer:
dₒ/dᵢ = 0.32
Step-by-step 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