Calculate a: Dist. b/w Lens Positions for 40 cm Object-Image Distance

[matt85]

The distance between an object and its image is fixed at 40.0 cm. A converging lens of focal length f = 3.62 cm forms a sharp image for two positions of the lens. What is the distance a between these two positions?

Determine:

The distance between these two positions a = ____cm

Could someone help me with the formula i want to be using?

 

[andrevdh]

The thin lens formula gives
$$\frac{1}{f}=\frac{1}{o}+\frac{1}{i}$$
with i the image distance and o the object distance. Now say you find a position between the object and fixed screen (image position) such that you get a sharp image on the screen. The object image is now o and the image distance i while the sum of these two being 40 cm. But according to the formula if you make the object distance i the image distance should be o! Which gives you the other position of the lens where you should get a sharp image on the screen. In the second case the object distance will therefore be i and the image distance will be o.

 

[andrevdh]

I would guess that with a mech advantage of 2 you would have problems lifting your lecturer! Three would give you a fighting chance!