An object is placed a distance of 13.5 cm to the left of a thin converging lens

Question

An object is placed a distance of 13.5 cm to the left of a thin converging lens of focal length f = 7.80 cm, and a concave spherical mirror with radius of curvature +16.0 cm is placed a distance of 41.2 cm to the right of the lens (see figure below). What is the location of the final image formed by the lens-mirror combination as seen by an observer positioned to the left of the object? cm to the left of the mirror What is the magnification of the final image as seen by an observer positioned to the left of the object? (Include the sign of the value in your answer.) Is the final image formed by the lens-mirror combination upright or inverted? upright inverted

Explanation / Answer

using formula for lens

1/f = 1/di + 1/do

1/di = 1/7.8 - 1/13.5

di = 18.47 cm

now object (image formed by lens) distance for mirror = 41.2 - 18.47 = 22.73 cm

focal length of mirror = 16/2 = 8 cm

1/di = 1/8 - 1/22.73

di = 12.34 cm to the left of the mirror [answer]

magnification = - di/do = - 12.34/(13.5 + 41.2) = - 0.225

and image is inverted.

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