Question

For a given focal length, f, for what values of the object distance, do, will the image distance, di, be negative?

(1/f)=(1/do)+(1/di)

Answer 1

As,given the equation,

1/f = 1/do + 1/di

The magnification ratio is simply the ratio of the image size to the object size. It is often calculated using the equation

M = hi / ho

In this equation, the variable M represents the magnification, the variable hi represents the image height, and the variable ho represents the object height. It ends up that the ratio of the image to object heights is equivalent to the ratio of the image to the object distance. And so the magnification equation is often written as

M = hi / ho = - di / do

Stating that the image is three times the size of the object is stating that the ratio hi/ho is either +3 or -3. Determining whether hi/ho is +3 or -3 demands an understanding of the sign conventions (as discussed in the above table). The ho value is always positive (for our purposes). The hi value is positive for upright images and negative for inverted images. Since this statement asserts that the image is real (and thus inverted), a -3 value must be assigned to the hi/ho ratio. Since hi/ho is equal to -di/do, the -3 value can be equated with -di/do.

do = (+1/3)•di or di = +3do