An object of height 20 cm is placed in front of a lens at a distance of 50 cm . Its virtual, diminished image is formed at a distance of 15 cm . Calculate the focal length of the lens.
Explanation
To calculate the focal length of the lens, we can use the lens formula: 1/f = 1/u + 1/v, where f is the focal length, u is the object distance, and v is the image distance. Given that u = 50 cm and v = -15 cm (since the image is virtual), we can plug in the values and solve for f: 1/f = 1/50 - 1/(-15) = 1/50 + 1/15 = (3+10)/150 = 13/150. Therefore, f = 150/13 = 30 cm.
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