An object 1 cm high produces a real image 2 cm high, when placed at a distance of 15 cm from a convex lens. calculate the position of the image and the magnification and also the focal length of lens.
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The position of the image is at - 30 cm, the magnification is 3 and the focal length is 30 cm.
Explanation:
Given data:
Height of object (ho) = 1 cm
Height of image (hi) = 2 cm
Object distance (u) = 15 cm
Now magnification = v/u = hi/ho = 2/1 (Since v/ -15 = 2/1)
=> v = - 30 cm
Magnification (m) = v/u = 30/15
m = 2
Using the lens formula:
1/f = 1/v - 1/u => 1/f = 1/-30 - (1/-15)
1/f = 1/-30 + 1/15
1/f = -1 +2/30
1/f = 1/30
f = 30 cm
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