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Q. An object 50 cm tall is placed on the principal axis of a convex lens. Its 20 cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens.


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Answer 1

magnification = height of image/height of object

= -20/50 = -2/5

As magnification = v/u


-2/5 = v/u

v= 10

-2/5 = 10/u

u = -10× 5/2 = -25


1/f = 1/v - 1/u

1/f = 1/10 +1/25

1/f = 5 + 2)/ 50

1/f = 7/50

f = 50/7

Answer 2

Solution :

We have provided with the height of object , height of image and Image distance .

Height of the Object ( h )  = 50 cm

Height of the image ( h' ) = -20 cm

Image Distance = 10 cm

Finding the Object distance

⇒ m = h'/h = v/u

⇒ u = ( v * h )/(h')

⇒ ( 10 * 50 ) /(-20)

⇒ -25 cm = u

Therefore , the required object distance is -25 cm

Finding the focal length of the lens

Focal length of lens = (1/F) = (1/v) - (1/u)

⇒ ( 1/F) = (1/10) - (1/(-25)

⇒ (1/F) = 7/50

⇒ 1/F = 7/50

⇒ F = 50/7 cm

⇒ F = 7.14 cm

Therefore , the focal length of the lens is 50/7 cm  or 7.14 cm