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Question
A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is
- a convex lens of focal length 20 cm, and
- a concave lens of focal length 16 cm?
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Solution
In the given situation, the object is virtual and the image formed is real.
Object distance, u = +12 cm
(a) Focal length of the convex lens, f = 20 cm
Image distance = v
According to the lens formula, we have the relation:
`1/"v" - 1/"u" = 1/"f"`
`1/"v" - 1/12 = 1/20`
`1/"v" = 1/20 + 1/12`
`1/"v" = (3 + 5)/60`
`1/"v" = 8/60`
v = `60/8`
∴ v = 7.5 cm
Hence, the image is formed 7.5 cm away from the lens, towards its right.
(b) Focal length of the concave lens, f = −16 cm
Image distance = v
According to the lens formula, we have the relation:
`1/"v" - 1/"u" = 1/"f"`
`1/"v" = 1/"f" + 1/"u"`
`1/"v" = 1/-16 + 1/12`
`1/"v" = (-3 + 4)/48`
`1/"v" = 1/48`
∴ v = 48 cm
Hence, the image is formed 48 cm away from the lens, towards its right.
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