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

[no idea]

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

 

[Doc Al]

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.

 

[M98Ranger]

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!