A 5 cm high object is placed at a distance of 25 cm from a converging lens of focal length of 10 cm. Determine the position, size and type of the image.

Answer

Given Height fo the object `(h_1)= 5 cm`
Focal length (f)= 10 cm
Distance of the object (u) =-25 cm
To find: Image distance (v)= ?
Height of the image `(h_2)=?`
Formula: `1/v-1/u= 1/f `

Explanation

(i) `1/v- 1/u= 1/f`
`therefore 1/v= 1/f+1/u`
`therefore 1/v=1 /10+1/(-25)`
`therefore 1/v =1/10 -1/25`
`therefore 1/v= (25-10)/(250)`
`therefore 1/v =15/250`
`therefore 1/v=3/50,v = 50/3 = 16.666`
`therefore v= 16.7 cm`
(ii) `h_2/h_1 = v/u`
`therefore h_2/5 = (50/3)/(-25)`
`therefore h_2 = - (50 xx5)/(3 xx25) = (-10)/(3) =- 3.333`
`therefore h_2 = -3.3 cm`
Position of image = 16.7 cm
Size of the image = 3.3 cm
Nature = Real and inverted.