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

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Question : 8
Total: 38
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,
1
v
−
1
u
 =
1
f
1
v
−
1
+12
 =
1
+20
 or
1
v
 =
1
20
+
1
12
 =
3+5
60
v =
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,

1
v
−
1
u
 =
1
f
1
v
−
1
+12
 =
1
−16
or
1
v
 = −
1
16
+
1
12
 =
−3+4
48
 =
1
48
v = + 48 cm
The image I is formed by diverged rays at 48 cm away from concave lens.
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