Splitting of a convex lens problem

[Krushnaraj Pandya]

Homework Statement

A thin convex lens of focal length 20 cm is split into two parts along the principal axis, now there is a 2mm gap between the top and bottom parts, an object O is placed at 10 cm from the lens, the distance between the two virtual images will be?

Homework Equations

1/v - 1/u =1/f

The Attempt at a Solution

Cutting along principal axis, focal length remains same. Using lens formula I got v= -20, I think this will then act as an object but using this value gives v2=infinity which isn't correct- how do I proceed?

 

[BvU]

v = -20 for the upper half, or for the lower half ?
Make a sketch ...

 

[haruspex]

the distance between the two virtual images

What do you think this refers to? In which direction is this distance?

 

[Krushnaraj Pandya]

v = -20 for the upper half, or for the lower half ?
Make a sketch ...

What do you think this refers to? In which direction is this distance?

Ok, so the distance is the gap along y-axis The magnification is 2 but I'm confused whether the base of the two images will be on the old principal axis or along the horizontal line containing the straight horizontal part of the half-lens. I suppose if it were on the old axis, there'd be no distance so it has been shifted along with the lens which would give the answer as 2mm but how these images are getting separated just isn't clicking in my mind and I'm having trouble even trying to think how to make a sketch

 

[BvU]

Ok, so the distance is the gap along y-axis

You don't give us a clue what axis that is.
You also don't post a sketch for good reasons:

I'm having trouble even trying to think how to make a sketch

because I suspect you can't make sense of

is split into two parts along the principal axis

So let's start with a sketch of the situation before the splitting. Can you post that and make clear what the principal axis is ?

 

[haruspex]

whether the base of the two images will be on the old principal axis or along the horizontal line containing the straight horizontal part of the half-lens.

Or maybe neither.
If you follow a ray from where the object sits on the principal axis through the middle of the lens, where does it meet the image?
When the lens is split there are two copies of the old middle. If you now draw the rays to each of these points, where do they meet the respective images?