The lens and mirror in figure are separated by 1 m and have a focal length of 81

Question

The lens and mirror in figure are separated by
1 m and have a focal length of 81.2 cm and
-75.2 cm, respectively.
If an object is placed 1 m to the left of
the lens, locate the final image. The object
is illuminated from the left, and the image is
viewed from the left.
Answer in units of cm.

Determine the overall magnification.

What is the nature of the image?
1. virtual, inverted, smaller
2. real, upright, larger
3. virtual, inverted, larger
4. virtual, upright, smaller
5. real, upright, smaller
6. virtual, upright, larger
7. real, inverted, smaller
8. None of these
9. real, inverted, larger

Explanation / Answer

The focal length of the lenses f1 = 81.2 cm and the focal length of the mirror f2 = -75.2 cm The object distance p = 1m then from lens formula          1/f1 = 1/p + 1/q then the image distance is      q = pf1 /p -f1          = (100cm)(81.2cm) / 100- 81.2          = 431.9 cm magnification m1 = - 431.9/100 = - 4.32 then the object distance for mirror p' = 431.9 - 100 = 331.9 cm then image distance q' = (331.9cm) (-75.2) / 331.9 + 75. 2                                   = - 61.3 cm magnification m = 61.3 / 331.9 = 0.18 then the over all magnification M = (-4.32)(0.18) = 0.77 Since the object distance is negtive so virtual, uprigth and smaller

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