An observer to the right of a mirror-lens combination shown below sees two real
ID: 1298304 • Letter: A
Question
An observer to the right of a mirror-lens combination shown below sees two real images that are the same size and in the same location (one image is formed by the light from the object passing through only the lens, the other image is formed from the light first being reflected by the mirror, and then passing through the lens). One image is upright, and the other is inverted. Both images are 1.50 times larger than the object. The lens has a focal length of 10.0 cm. The lens and mirror are seperated by 40.0 cm. Determine the focal length of the mirror.
Explanation / Answer
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An observer to the right of the mirror-lens combination shown inthe figure below sees two real images that are the same size and inthe same location. One image is upright and the other is inverted.Both images are 1.50 times larger thanthe object. The lens has a focal length of 10.6 cm. The lens and mirror are separated by 40.0cm. Determine the focal length of the mirror.
Answer
focal length of the lens f1 = 10.6 cm
for the given probloem let p1 bethe object distance and q1 is the image distance
the magnification is 1.50
the magnification M is given by
M = - (q1 /p1)
= - 1.50
q1 = 1.50 p1
the thin lens equation is given by
(1 / f) = (1 / p1) + (1 /q1)
(1 / 10.6 cm) = (1 / p1) + (1 / 1.50p1)
p1 = ......... cm
in the figure the upright image is formed bythe light that passes through the lens after reflecting
from the mirror
now the object for the lens in this uprightimage formation is the image formed by the mirror
so to get an upright image at the samelocation as the inverted image the image formed by the
mirror must be located at the position ofthe original object so the object and image distance for
the mirror are equal and their common valueis
qmirror - pmirror =40.0 cm - p1
= ....... cm
using the mirror equation we get
(1 / pmirror) + (1 /qmirror) = 2 / R
= (1 / fmirror)
solve for the focal length of the mirror
fmirror = ......... cm