Why 0.3m From Lens Is Optimal Focus?

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The optimal focus distance of 0.3m from the lens is crucial for achieving a clear image when a plane mirror is positioned 0.2m behind the lens. When an object is placed at the focal point, rays emanating from it pass through the lens and emerge parallel. These parallel rays then reflect off the mirror and reconverge upon returning through the lens, forming a coherent image. Understanding the behavior of light rays in this setup is essential for accurate image formation. This discussion emphasizes the importance of ray diagrams and the thin lens formula in optics.
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Homework Statement
A lens has a focal length of 0.3m. A plane mirror is placed 0.2m behind the lens. Where must an object be placed, for its image to coincide with its position?
Relevant Equations
Ray diagrams
thin lens formula
Apparently, it must be placed at the focus (0.3m away from the lens). Why is this so?
 
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phantomvommand said:
Homework Statement:: A lens has a focal length of 0.3m. A plane mirror is placed 0.2m behind the lens. Where must an object be placed, for its image to coincide with its position?
Relevant Equations:: Ray diagrams
thin lens formula

Apparently, it must be placed at the focus (0.3m away from the lens). Why is this so?
If the object is at the focus, what can you say about the rays from a given point on the object after they have passed through the lens?
Follow their path on to the mirror and back through the lens.
 
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haruspex said:
If the object is at the focus, what can you say about the rays from a given point on the object after they have passed through the lens?
Follow their path on to the mirror and back through the lens.
Won't the rays that emerge from the lens all be parallel to each other? But the rays hit the mirror at different points. How will the reflected paths then reconverge to form the image?
 
haruspex said:
If the object is at the focus, what can you say about the rays from a given point on the object after they have passed through the lens?
Follow their path on to the mirror and back through the lens.
I see what you mean. Thank you very much
 

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