An object of height 20 cm is placed at a distance of 50 cm from a lens. Its virtual, diminished image formed at a distance of 15 cm. (a) Name the lens and (b) calculate the focal length of the lens.
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An object of height 20 cm is placed at a distance of 50 cm from a lens. Its virtual, diminished image formed at a distance of 15 cm. (a) Name the lens and (b) calculate the focal length of the lens.
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Answer:
(a) The lens in this case is a concave lens.
(b) To calculate the focal length of the lens, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the distance of the image from the lens (in this case, 15 cm)
- u is the distance of the object from the lens (in this case, 50 cm)
Let's substitute the values into the formula and calculate the focal length:
1/f = 1/15 - 1/50
To simplify the calculation, we can find the common denominator:
1/f = (50 - 15)/(15 * 50)
1/f = 35/750
Now, let's take the reciprocal of both sides to find the focal length:
f = 750/35
f ≈ 21.43 cm
Therefore, the focal length of the concave lens is approximately 21.43 cm.
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