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

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Question : 19
Total: 38
The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3 m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?
Solution:  
Let the object be placed x m in front of lens the distance of image from the lens is(3 – x) m.
Applying lens formula,
1
v
−
1
u
 =
1
f
1
(3−x)
−
1
−x
 or
1
(3−x)
+
1
x
 =
1
f
 or
x+3−x
x(3−x)
 =
1
f
 or 3f = 3x - x2
so, x2 - 3x + 3f = 0
Now x =
+3±√9−4×(3f)
2
 or x =
+3±√9−12f
2
Condition for image to be obtained on the screen, i.e., real image.
9 – 12f ≥ 0 or 9 ≥ 12f or f ≤ 0.75 m.
So, maximum focal length is 0.75 m.
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