Physics- Lens Questions

[NYKnick]

An object is placed upright on the axis of a thin convex lens at a distance of four focal lengths (4f) from the center of the lens. An inverted image appears at a distance of 4/3f on the other side of the lens. What is the ratio of the height of the image to the height of the object?

a. 1/3
b. 3/4
c. 4/3
d. 3/1

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[NYKnick]

I was having some trouble with this problem and was wondering if anyone could give me a detailed explanation to why the answer is A. thank you!

 

[manno]

hey, the question is basically asking for the magnification (M) , which is equal to f/f-o, where f = focal length of the lens and 0 = object distance. For the question M = f/f-4f = f /-3f = -1/3, therefore the answer is A. Alternatively , M = - image distance/object distance = - 4f/3 x 1/4f = -1/3. I hope this helps.