(a) A 5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 30 cm. Find the position, nature and size of the image formed.
(b) Draw a labelled ray diagram showing object distance, image distance and focal length in the above case.
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(a)
ho = +5 cm
f = +20 cm
u = -30 cm
We know that in a lens,
1/v - 1/u = 1/f
1/v = 1/f + 1/u
= 1/20 + 1/-30
= 1/20 - 1/30
= (3 - 2)/60
= 1/60
Therefore, v = 60 cm.
Since v is +ve, the image formed is real and inverted.
The image is formed 60 cm behind the lens.
m = v/u = 60/-30 = -2
But, m = hi/ho
Therefore, hi = m * ho = -2 * 5
hi = -10 cm
Thus, the image is -10 cm tall. Here, -ve sign shows that the image is real and inverted.
(b) refer to the attachment.
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