A thin, converging lens whose focal length is 78 cm is placed 5.2 m from a conve

Question

A thin, converging lens whose focal length is 78 cm is placed 5.2 m from a convex spherical mirror whose focal length is 52 cm (see figure below). For an object placed 1.5 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

(b) the magnification of the image


(c) the nature of the image (Select all that apply.)

real

virtual

upright

inverted

enlarged

reduced

Explanation / Answer

For the lens :

do = object distance = 1.5 m

f = focal length = 0.78 m

di = image distance

using the lens equation

1/di + 1/do = 1/f

1/di + 1/1.5 = 1/0.78

di = 1.625 m

mlens = magnification by lens = hi/ho = - di/do = - 1.625 / 1.5 = -1.08

For the mirror :

do = object distance = distance between lens and mirror - image distance = 5.2 - 1.625 = 3.575 m

f = focal length = - 0.52 m

di = image distance

using the mirror equation

1/di + 1/do = 1/f

1/di + 1/3.575 = 1/(-0.52)

di = - 0.454 m

image formed is 0.454 m from the mirror towards right.

b)

for mirror :

ho' = hi = - 1.08 ho

magnification = hi'/ ho' = - di/do = - (-0.454) / 3.575

hi'/ (- 1.08 ho ) = - (-0.454) / 3.575

hi'/ ho = - 0.14 = magnification of final image

c)

the image is virtual, inverted and reduced in size

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