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 formed first by reflection and then by refraction.

question:The position of the final image, measured from the mirror, in cm, is closest to:

According to the solution ,The answer is 114cm.

But according to my book" In lens combinations, the image formed by the first lens becomes the object for the second lens (this is where object distances may be negative)".

So if the object distance is "negetive" = -92.2 the answer q would be 90cm instead 114cm. (1/-92.2)+1/q=1/30

Please tell me why the ans is 114cm

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 <<<----------answer

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