A convex lens is needed to produce an image that is 0.60 times the size of the object and located 30 cm from the lens on the other side. What focal length should be specified?

Answer 1

Since the image is located on the other side of the lens the magnification is negative so m=-.6 = - s_i/ s_o where s_i is the image distance and s_o is the object distance. So s_o = s_i / .6 s₀ = 50 cm for an image distance of 30 cm. Using the optics equation relating the focal distance to the object and image distance where 1/s_o + 1/s_i =1/f the equation becomes 1/50 + 1/30 =1/f solving for f gives f= 50*30/ 80 and f=18.75 cm.