Trying to find the image of an object reflected through a lens and

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The discussion revolves around determining the final image location and height of a 1 cm tall object placed at x = -6 cm, using a lens with a focal length of 4 cm and a plane mirror at x = 7 cm. The initial analysis shows that the image formed by the lens is inverted at approximately 12 cm. After reflecting off the mirror, the virtual object distance is calculated to be 5 cm behind the mirror, leading to a real image formed at 2 cm from the lens. The participants emphasize the importance of ray diagrams for visualizing the light paths and reflections involved in the process. The final image is confirmed to be real and located at 2 cm from the lens.
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then through a plane mirror (I could put that all down in the title!)

Homework Statement



A bright object 1 cm tall is located at x = -6 cm. There is a thin lens atx = 0 with focal length f = 4 cm, and a plane mirror located at x = 7 cm. Light from the object passes through the lens, reflects off the mirror, and then passes through the lens again to form an image.

(a) Where is the final image located? Is it real or virtual?

(b) What is the height of the final image?

Homework Equations



I drew a ray diagram for when the object is reflected through the lens. Disregarding the plane mirror, I found image is inverted at about 12 cm. I know that that the rays should reflect off the plane mirror (following the law of reflection), but when I draw my rays, the focal ray, which is perpendicular to the plane mirror, is reflected in the same direction it hit the mirror. However my parallel and central rays hit the bottom of the lens and then I'm not quite sure what the rays should look like after that.

The Attempt at a Solution



Drew my ray diagram for when the object is reflected through the lens. Not quite sure how to work around the plane mirror...
 
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Mirror is placed at 7 am from the lens. So the distance of the virtual object behind the mirror is 5 cm. In the mirror object distance equal to the image distance. If the object is real, image is virtual. And If the object is virtual, the image is real. Hence the image is real at 2 cm from the lens. Now find the final image.
 
Since most of your work is a ray diagram it would be good if you post it here...
 
rl.bhat said:
Mirror is placed at 7 am from the lens. So the distance of the virtual object behind the mirror is 5 cm. In the mirror object distance equal to the image distance. If the object is real, image is virtual. And If the object is virtual, the image is real. Hence the image is real at 2 cm from the lens. Now find the final image.

Okay, that makes sense. Thanks for your help!
 
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