Question

. If an object of 7 cm height is placed at a distance of 12 cm from a
convex lens of focal length 8 cm, The height of the image is :
(1) 2 cm (2) 24 cm (3) 14 cm (4) 30 cm
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Answer 1

height wil be 14cm..

Here, h1=7 cm, u=−12 cm, f=8 cm, h2=?, v=?

The formula for calculating focal length is given as,

1v−1u=1f

or, 1v=1f+1u

or, 1v=18−112=3−224=124

thereforev=24 cm

So the position of the image is 24 cm and as v is positive, the image is real.

Now, magnification, m=h1h2=vu

or, h27=24−12

or, h2=−14 cm

Answer 2

Answer:

Height of object = 7 cm

Distance of object from lens(u) = -12 cm

Focal length(f) = 8 cm

1/f = 1/v - 1/u

=> 1/8 = 1/v - 1/-12

=> 1/v = 1/8 - 1/12

=> 1/v = (12-8)/96

=> 1/v = 4/96

=> 1/v = 1/24

v = 24 cm

h/h' = -v/u

=> h/7 = -24/-12

=> h/7 = 2

=> h = 14 cm

Answer: (3) 14 cm

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