A \"floating object\" illusion can be produced by two concave, parabolic mirrors

Question

A "floating object" illusion can be produced by two concave, parabolic mirrors, each with a focal length of 7.5 cm, facing each other so that their centers (vertices) are 7.5 cm apart. If an object sits on the bottom mirror an image forms at the opening in the top mirror. Use the mirror equation (twice) to show that the final image forms at that location, and describe the image (real/virtual, upright/inverted/reduced/enlarged). Draw three rays that show the path of the light from the object to the image.

Explanation / Answer

let for the first mirror, u=7.5 cm and f =7.5 cm

using 1/f = 1/u +1/v

1/v = 1/u -1/f

v = uf/(-u-f)

v = 7.5* 7.5/(7.5+7.5)

v =-3.75 cm

so this acts as object for second mirror

so v = uf/(u+f)

v = 7.5 * 3.75/(7.5-3.75)

v = 7.5 cm

thus image is formed at focal point,

image wud be virtual, upright and reduced

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