Question

A 2 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 10 cm. The distance of the object from the lens is 15 cm. find nature , position and size of image. Also, find it's magnification.

Answer 1

Hey!

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Object's size (h1) = 2 cm
Focal length of convex lens (f) = 10 cm
Object distance from the lens (u) = -15 cm
Image distance ( v) = ?
Image size (h2) = ?

We know,

1/v - 1/u= 1/f

1/v = 1/f + 1/u

1/v = 1/10 - 1/15

1/v = 1/30

Thus, v = 30 cm

Now, v = 30 cm, 'v' is positive, that means the image is formed on the right side of the lens. That's why it is REAL and INVERTED.

Now, magnification =?

Linear magnification (m) = Size of image / Size of object = h2 / h1 = v/u

m = h2/2 = 30/-15

m= h2 × -15 = 30×2

m = -15 h2 = 60

h2 = 60 / -15

h2 = -4 cm

Size of the image = -4 cm
It's in negative , that means that the image is INVERTED.

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Hope it helps...!!!

Answer 2

Hey!!!!

We have, for a convex lens
h = +2cm
f = +10cm
u = -15cm
h' = ?
m = ?

Thus by lens formula

=> 1/f = 1/v - 1/u

=> 1/10 = 1/v + 1/15

=> 1/v = 1/10 - 1/15

=> 1/v = 1/30

Thus v = +30 cm

Now m = +v/u

Thus m = -30/15

=> m = -2

Thus the image will be real, inverted and enlarged

Also m = h'/h

=> -2 = h'/2

=> h' = -4cm

Thus the size of the image will be 4 cm.

Hope this helps!