How Is the Focal Length Determined When an Object and Its Image Coincide?

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The focal length of a convex lens can be determined using the lens equation, 1/f = 1/do + 1/di. In this scenario, with an object placed 20 cm in front of the lens and an inverted image coinciding with the object, both do and di equal 20 cm. Substituting these values into the equation yields a focal length of 10 cm. The convex lens successfully creates an inverted image at the same position as the object when positioned 20 cm away. Thus, the focal length is confirmed to be 10 cm.
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An object pin is placed 20cm in front of a convex lens which is 10 cm away from a plane mirror . An inverted image is found at the same position of the object(above the object).
What is the focal length?
thanks
 
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Here are a few hints. Is the image formed by the lens real or virtual? What does a plane mirror do?

Figure out where the image would be if the mirror wasn't there.
 


The focal length can be calculated using the lens equation, which states that 1/f = 1/do + 1/di, where f is the focal length, do is the distance of the object from the lens, and di is the distance of the image from the lens. In this case, do = 20cm and di = 20cm, since the image is found at the same position as the object. Plugging these values into the lens equation, we get: 1/f = 1/20cm + 1/20cm = 2/20cm. Solving for f, we get a focal length of 10cm. This means that the convex lens has a focal length of 10cm, and it is able to create an inverted image at the same position as the object when placed 20cm in front of it. I hope this helps!
 
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