A thin, converging lens whose focal length is 81 cm is placed 5.4 m from a conve

Question

A thin, converging lens whose focal length is 81 cm is placed 5.4 m from a convex spherical mirror whose focal length is ?51 cm (see figure below). For an object placed 1.1 m to the left of the lens, determine the location of the image formed by the mirror, the magnification of the image, and the nature of the image (real/virtual, upright/inverted, enlarged/reduced). Hint: Use the image formed by the lens as the object for the mirror.

(a) the location of the image formed by the mirror:

|distance| _______cm

(b) the magnification of the image _____

Explanation / Answer

for the converging lens

1/f = 1/do + 1/di

1/81 = 1/110 + 1/di

1/di = 1/81 - 1/110

di = 307.2 cm = 3.072 m distance of image from converging lens.

now this image is object of convex mirror

so distance of object for convex mirror = 5.4 - 3.07 = 2.33 m = 233 cm

mirror formula

1/f = 1/di + 1/do

1/di = 1/-51 - 1/233

di = - 41.84 cm   { answer of a}

b)

magnificaton = - di/do = - (-41.84)/233 = 0.179

and hi/ho = -di/d

hi/ho = 0.179

so image of mirror is reduced.

magnification is positive so image is upright.

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