Converging Lens and Plane Mirror Question

[Quattad]

Homework Statement

A real object is put in-between a convex lens (f = 30.0cm) and a plane mirror as shown in the figure below. Two images of the object are observed : a real image 50.0cm to the left of the lens and a virtual image to the right of the lens. The size of the virtual image is 3.00 times that of the real image.

(a) Find the location of the real object with respect to the lens. What is its size comparing with the virtual image?
(b) Find the location of the mirror with respect to the lens.

I've attached a picture of the question for easy reference.

Homework Equations

The Attempt at a Solution

I know that there are two images being formed.
The virtual image is formed in an imaging process that involves only the lens and the object. Since d_object < f = 30, the image will be virtual, upright and enlarged.
The real image is formed in an imaging process that involves both the lens and the planar mirror. The object is reflected about the plane of the planar mirror, forming a virtual object behind the surface of the mirror. This virtual image acts as the object for the converging lens and forms a real, inverted and reduced image on the left of the converging lens.

However, I'm not too sure on how to use the size of the virtual and real image to find the location of the real object.

Any help will be greatly appreciated!

 

[J Hann]

Try the real object distance as 2 D + O where O is the distance of the real object from the lens
and D the distance of the real object to the mirror.
This (O) is also the object distance for the virtual image.
Together with the thin lens equations and the equation for magnification which depends only
object and image distances you should be able to solve the problem.
Be careful with signs regarding the magnification especially where the virtual image is 3X the real image
because these are two independent quantities that only depend on their associated object and image distances.