An optical system comprises in turn, from left to right: an observer, a lens of

Question

An optical system comprises in turn, from left to right: an observer, a lens of focal length +30 cm, an erect object 20 mm high, and a convex mirror of radius 80 cm. The object is between the lens and the mirror, 20 cm from the lens and 50 cm from the mirror. The observer views the image that is formed first by reflection and then by refraction. What is the magnification of the final image form by this system? Is the final image inverted or it has the same orientation as the object?

Explanation / Answer

here the image is first formed by mirror

1/s1 + 1/s1' = 1/f1

1/50 + 1/s1' = -1/40

s1' = -22.22 cm

for lens

s2 = (20+50) + 22.22

s2 = 92.22 cm

1/s2 + 1/s2' = 1/f2

1/92.22 + 1/s2' = 1/30

s2' = 44.44 cm to the left of the lens

position from the mirror = 44 + 70 = 114 cm

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