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) a convex lens of focal length 20 cm, and (b) a concave lens of focal length 16 cm?
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`
= `(3 + 5)/60`
= `8/60`
∴ v = `60/8` = 7.5 cm
Hence, the image is formed 7.5 cm away from the lens, toward 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" = -1/16 + 1/12`
= `(-3 + 4)/48`
= `1/48`
∴ v = 48 cm
Hence, the image is formed 48 cm away from the lens, toward its right.
