# Ray diagram for diverging lens with both object and image that are virtual

I do not understand how to proceed in order to create the ray diagram of the case of a diverging lens where both object and image are virtual, that is $f<0$ , $p<0$ with $p<f$ (otherwhise the image wuold be real.

I did not find this particular case of ray diagram in any textbook so I would like to know where to find it or how to build it on my own.

• Which way is light travelling through the optical system you have sketched? – DJohnM May 7 '17 at 2:43
• Have you seen the ray diagrams here? It shows the case of a real object inside the focal point leading to a virtual image outside. I am not sure how you can have a "virtual object" - I thought an object can only ever be real, it's the image that could be virtual. A virtual image can't be projected on a screen - but what is a virtual object? – Floris May 7 '17 at 3:45

The top diagram shows the formation of the virtual object where converging rays are prevented from meeting by the diverging lens.

Then those converging rays are made to diverge by the lens and so a virtual image is formed.

Update as a result of a comment from @Floris.

I included a converging lens just to check the orientation of the virtual object and the virtual image for the diverging lens.

As pointed out by @Floris the diagram that the OP had the virtual object and the virtual image both upright so I investigated whether that was possible by moving the position of the virtual object relative to the focal point of the diverging lens.

Rays labelled $1$ have the virtual object in the focal plane of the diverging lens and that produces an image at infinity.

Rays labelled $s$ have the virtual object outside the focal point of the diverging lens and that always produces an inverted and virtual image.

Rays labelled $3$ have the virtual object inside the focal point of the diverging lens and that produces an upright image which is real.

• Thanks a lot, it made things clearer! One thing if I may, the direction of the arrows in the picture are in that way to take in to account that the image and the object are virtual? Because usually rays come out from object and goes towards the image but in the picture is the contrary – Sørën May 7 '17 at 11:30
• In the original diagram both virtual object and virtual image are upright but your construction has one flipped relative to the other? – Floris May 7 '17 at 11:44
• @Floris I did investigate that very point but came to the conclusion that it could be done. I have added an update to my answer to show this. – Farcher May 7 '17 at 14:39