Question

A 10cm tall image is projected on a screen 50cm away from a convex lens of focal length 20cm.Find the position and size of the object.

Answer 1

Answer:

Explanation:

The given quantities are  

Height of the object h = 50 cm

Height of the image formed h’ = -20 cm

Image distance v = 10 cm

The image distance is the distance between the position of convex lens and the position where the image is formed.

The ‘focal length’ of a convex lens can be found using the below formula

Here f is the focal length, v is the image distance which is known to us and u is the object distance.

The object distance is the distance between the ‘object position’ and the lens position. To determine the focal length, first we should find the object distance.

From the magnification equation, we know that

Thus,

So, the object distance will be

So the focal length will be

Thus the focal length of the convex lens is 7.14 cm

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Answer 2

Answer:

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Explanation:

The focal length f =20cm  

height of image is 10cm  

as screen is 50cm away so the image distance v = 50cm

using lens formula

1/v-1/u=1/f

1/50-1/u=1/20

1/50-1/20=1/u

0.02-0.05=1/u

-0.03=1/u

u=-33.3cm

magnification of the lens

hi/ho=-v/u

ho=-hi*u/v

h0=6.66 cm

diminished virtual and erect.