When the object is placed at 16 cm in front of a convex lens of focal length 24 cm , the image is formed at _____.
Answers
Answer:
For a convex lens, a magnified image is obtained for three positions of object:
i. When object lies between f and 2f
ii. When object is at f
iii. When object lies between f and lens
Out of these positions, when object is at f, image will be formed at infinity and m=∞.
For other two positions m is not equal to ∞, therefore there is no other position for which m=∞ and given that m is equal for two positions of object i.e. object is not at f because we have no other position for m=∞.
Let in first position object lies between f and 2f.
Given: u=−16cm
From lens equation:
v=
u+f
uf
v=
−16+f
−16f
since f<u<2f, v will be +ive ,
hence, m=
−u
v
=
−16
(
−16+f
−16f
)
...................eq1
Let in second position object lies between f and lens.
Given: u=−8 cm
From lens equation:
v=
u+f
uf
v=
−8+f
−8f
since u<f, v will be -ive,
hence, m=
−u
−v
=
−8
−(
−8+f
−8f
)
.........................eq2
By eq1 and eq2:
−16
−16+f
−16f
=
−8
−(
−8+f
−8f
)
f=12 cm
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Image will form behind the object (on the left side of lens)