What Is the Focal Length of the Concave Lens in This Lens-Mirror Combination?

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The problem involves a convex lens forming a real image at 50 cm, with a concave lens placed 10 cm behind it on the image side. A plane mirror reflects the image back through the concave lens, resulting in the final image coinciding with the original object. The focal length of the concave lens needs to be determined using the lens formula. The initial value of v is set at +50 cm for the convex lens, which serves as the object for the concave lens. Further progress requires a ray diagram to visualize the setup and calculate the focal length.
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Homework Statement


a convex lens forms a real image of a point object at a distance of 50 cm from convex lens. a concave lens is placed 10 cm behind convex lens on image side. on placing a plane mirror on the image side and facing the concave lens it is observed that final image now coincides with the object itself. find focal length of concave lens.

Homework Equations


1/f = 1/v - 1/u

The Attempt at a Solution


v= +50cm for convex lens as real image is formed on opposite side to object.
this acts as object for concave lens
unable to proceed further
 
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Try drawing a ray diagram.
 

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