Two concave mirrors on a table

[Father_Ing]

Homework Statement

Two concave mirrors are placed 40 cm apart and are facing each other. A point object lies between them at a distance of 12 cm from the mirror of focal length 10 cm. The other mirror has a focal length of 15

Relevant Equations

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I'm currently confused in determining whether an image formed by the 1st mirror (the left one) is a real or virtual object for the 2nd mirror.

Here is the solution manual:

This is what I have in my mind:
Since the object is located between the focus and radius point of the first mirror, the image formed after the first reflection must be real, both as an image and as an object for the 2nd mirror (although the position is 20 cm from the "back" of the said mirror). And in order to see this image, we can place a screen at distance 20cm from the 2nd mirror.

Note that what I mean by "the back" above, is not behind the mirror (virtual).

However, in the solution manual, it says that the image formed is virtual for the 2nd mirror.
I don't understand why the image is inside of the "mirror world" instead of the real world.

Any help would be appreciated!

 

[hutchphd]

No. It says that he image from the first mirror forms a virtual object for the second.

 

[Lnewqban]

Copied from:
https://courses.lumenlearning.com/boundless-physics/chapter/mirrors/

"An image formed by reflection may be real or virtual. A real image occurs when light rays actually intersect at the image, and is inverted, or upside down. A virtual image occurs when light rays do not actually meet at the image. Instead, you “see” the image because your eye projects light rays backward. A virtual image is right side up (upright)."

 

[vela]

However, in the solution manual, it says that the image formed is virtual for the 2nd mirror.
I don't understand why the image is inside of the "mirror world" instead of the real world.

It's because you don't have actual light rays emanating from point $I_1$ and reflecting off the second mirror.

When you look at mirror 2, forget about mirror 1. You don't care if mirror 1 forms a virtual or real image. All you care about is where the image forms in relation to mirror 2. If the image formed by mirror 1 is in front of mirror 2, the object is real. If it's behind, the object is virtual.

Frankly, I'm not sure how useful this concept of a virtual object is. All you really need to know is that the image formed by the first mirror, regardless of whether it's real or virtual, become the object for the second mirror.

 

[hutchphd]

Frankly, I'm not sure how useful this concept of a virtual object is. All you really need to know is that the image formed by the first mirror, regardless of whether it's real or virtual, become the object for the second mirror.

I am not big on "naming" stuff. But drawing the ray trace for a "virtual object" can be a little tricky and so it is bit of nomenclature that I have found to be useful. It means "prepare to be confused when you draw the ray trace." Of course no one seems able to draw a ray trace anyway.

 

[guv]

Homework Statement:: Two concave mirrors are placed 40 cm apart and are facing each other. A point object lies between them at a distance of 12 cm from the mirror of focal length 10 cm. The other mirror has a focal length of 15
Relevant Equations:: -

I'm currently confused in determining whether an image formed by the 1st mirror (the left one) is a real or virtual object for the 2nd mirror.

Here is the solution manual:
View attachment 297963

This is what I have in my mind:
Since the object is located between the focus and radius point of the first mirror, the image formed after the first reflection must be real, both as an image and as an object for the 2nd mirror (although the position is 20 cm from the "back" of the said mirror). And in order to see this image, we can place a screen at distance 20cm from the 2nd mirror.

Note that what I mean by "the back" above, is not behind the mirror (virtual).

However, in the solution manual, it says that the image formed is virtual for the 2nd mirror.
I don't understand why the image is inside of the "mirror world" instead of the real world.

Any help would be appreciated!

The sign convention you will need for this is the object distance.

When light comes from the same side as the object the object distance is positive; negative other wise.

Images can be treated as objects for secondary lens. Use the above convention to figure out the sign then proceed to use lens equation.

 

[Father_Ing]

If we look at the 2nd mirror, could we see the virtual object?

 

[hutchphd]

If we look at the 2nd mirror, could we see the virtual object?

An image in a mirror is a virtual object, which can in turn be used to create another image in a second mirror. All objects created in a series of mirrors are virtual objects.