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NCERT Class XII Chapter
Ray Optics and Optical Instruments
Questions With Solutions

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Question : 8 of 38
Marks: +1, -0
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:  
(a) The convex lens is placed in the path of convergent beam.
Using lens formula, 1v−1u\frac{1}{v} - \frac{1}{u} = 1f\frac{1}{f}
1v−112\frac{1}{v} - \frac{1}{12} = 120\frac{1}{20} or 1v\frac{1}{v} = 120+112\frac{1}{20} + \frac{1}{12} = 3+560\frac{3+5}{60}
v = 608\frac{60}{8} = + 7.5 cm
The image I is formed by further converging beams at a distance of 7.5 cm from lens.
(b) A concave lens is placed in the path of convergent beam, the concave lens further diverge the light.
Using lens formula,
1v−1u\frac{1}{v} - \frac{1}{u} = 1f\frac{1}{f}
1v−112\frac{1}{v} - \frac{1}{12} = 1−16\frac{1}{-16}
or 1v\frac{1}{v} = −116+112-\frac{1}{16} + \frac{1}{12} = −3+448\frac{-3+4}{48} = 148\frac{1}{48}
v = + 48 cm
The image I is formed by diverged rays at 48 cm away from concave lens.
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