An object is placed vertically at a distance of 20 cm from a convex lens. If the height of the object is 5 cm and the focal length of the lens is 10 cm, what will be the position, size and nature of the image? How much bigger will the image be as compared to the object?

Answer

Given : Height of the object `(h_1)=5 cm`
Focal length (f)=10 cm
Distance of the object (u)=-20 cm
To find: Image distance (v)=?
Height of the image `(h_2)= ?`
Magnigication (M)= ?
(i) `1/v -1/u =1/f`
(ii) `h_2/h_1 = v/u`

Explanation

(i) `1/v- 1/u =1/f `
`therefore 1/v =1/(-20)+1/10=- 1/20 +1/10`
`therefore 1/v = (10+20)/(20 x10)`
`therefore 1/v = (10)/(200)`
`therefore v= 20 cm`
(ii) `h_2/h_1 = v/u`
`therefore h_2 = (v xx h_1)/(u)`
`therefore h_2 = (20 xx 5)/(-20)`
`therefore h= -5 cm`
(iii) `M = v/u = 20/(-20) =-1`
`therefore M=- 1`
The object and the image are of the same size. Image is real and inverted