Optics - Adding magnification in an optical system

[nordmoon]

Homework Statement

I have a system like image below

An object 1 (OP = Object plane) is projected onto the image plane 1 (IMP) where an eye is located, with a beam splitter (BS). This eye is also looking at some object at distance far away. I would like to magnify this image of the object at the distance. How can I do this?

Homework Equations

Lens formula,

1/OP + 1/IMP = 1/f.

Where the magnification is M = -IMP/OP or h_image/h_object

OP = distance of object to lens
IMP = distance of image plane of object to lens
f = focal length of lens

The Attempt at a Solution

I think a biconvex lens would work to create the magnification of the image of the object you are looking at. However I am unsure how to use it when you might look at objects at different distances. If you are looking at an object at different distances does the focal length of the lens have to change with it?

And does the beamsplitter affect the image at the object at the distance?

EDIT: updated attempt of solution and equations.

 

[BvU]

I have a system like image below

Well now, does it work ? With the beam splitter as drawn ?
What is it that projects object 1 to an image plane ? Did you ever try to see something with your eye located at 'the image plane' (it doesn't work) ?

 

[nordmoon]

Ok I feel like i need to simplify this a bit.

My question is, if you have an biconvex lens and place it in front of your eye, you will see enlarged image of what you are looking at. Is this correct?
If you now look at different objects at different distances, is there a way to remain focus on the object with this lens and have same magnification? What would take to make this happen?
Would a beam splitter affect the system if placed in between the line of sight?

 

[BvU]

My question is, if you have an biconvex lens and place it in front of your eye, you will see enlarged image of what you are looking at. Is this correct?

Not really. What have you observed ? I take it you can find a reading glass or a camera lens to do the experiment ?