Atransparent photographic slide is placed in front of a converging lens with a focal length of 2.33 cm. an image of the slide is formed 13.0 cm from the slide. (a) how far is the lens from the slide if the image is real?

Explanation:

Let the slide be at a distance of u from lens . So the object distance is u.

Image distance  v = 13 - u .

Using lens formula

1/v -1/u = 1/f

1/ ( 13 - u) - 1 / u = 1 / 2.33

u - (13 - u )/u(13 -u ) = 1/2.33

2u - 13/ 13u - u² = 1/ 2.33

4.66 u - 30.29 = 13 u -u²

u² - 8.34 u - 30.29 = 0

u =  -2.73 cm

So lens will be at a distance of 2.73 cm  from the slide.