Find the focal length of a lens that produces an inverted im

Find the focal length of a lens that produces an inverted image five times the size of a small object placed on the optical axis, 18.5 cm from the lens.

Solution

let h_i be the size of the image and h_o be the size of the object.

d_o be the object distance and d_i be the image distance

from the given data h_i = 5 h_o   or hi/h_o  = 5 and d_o =18.5 cm

but h_i/h_o = - d_i/d_o

therefore - di/d_o = 5 or d_i = - 5 d_o

from the formula 1/f = 1/di + 1/do

focal length f = d_i d_o /( d_i + d_o)

= - 5 d_o²/ -5d_o + d_o

= - 5 d_o²/-4d_o

= 1.25 d_o

   ₌ 1.25 x 18.5 = 23.12 cm

hence the focal length of the lens is 23.12 cm