Answer:
19.6 cm.
Explanation:
From the question given above, the following data were obtained:
Focal length (f) = 13.8 cm
Magnification (M) = +2.37
Object distance (u) =.?
Next, we shall determine the image distance. This can be obtained as follow:
Magnification (M) = +2.37
Object distance (u) = u
Image distance (v) =?
M = v / u
2.37 = v / u
Cross multiply
v = 2.37 × u
v = 2.37u
Finally, we shall determine the object distance. This can be obtained as follow:
Focal length (f) = 13.8 cm
Image distance (v) = 2.37u
Object distance (u) =.?
1/v + 1/u = 1/f
vu / v + u = f
2.37u × u / 2.37u + u = 13.8
2.37u² / 3.37u = 13.8
Cross multiply
2.37u² = 3.37u × 13.8
2.37u² = 46.506u
Divide both side by u
2.37u² / u = 46.506u / u
2.37u = 46.506
Divide both side by 2.37
u = 46.506 / 2.37
u = 19.6 cm
Thus, the lens should be held at a distance of 19.6 cm.
