Question:
A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
Answer:
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
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,
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.
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