Please show me how the thin lens formula could be used to solve this problem. Th

Question

Please show me how the thin lens formula could be used to solve this problem. Thank you!

In the above figure, an object O is at a distance of three focal lengths from the center of a convex lens. What is the ratio of the height of the image to the height of the object? Complex living organisms transport materials, sense their environment, process signals, and respond to changes using processes that can be understood in terms of physical principles. How light and sound interact with matter Scientific Reasoning and Problem Solving A. 1/3 B. 1/2 This is a Physics question that falls under the content category "How light and sound interact with matter." The answer to this question is B because the ratio of the image height to the object height is equal to the ratio of the lens-image distance to the object-lens distance. According to the thin lens equation, the distance between the lens and the image is 3F' 1F/(3F - 1F) = (3/2)F, where F is the focal length. The ratio sought is then equal to (3/2)F/(3F) = 1/2. It is a Scientific Reasoning and Problem Solving question because you are asked to determine and use scientific formulas to solve problems. C. 2/3 D. 3/2

Explanation / Answer

object distance s = 3F

focal length = F

image distance = s'

from thin lens equation

1/s + 1/s' = 1/f

1/3F + 1/s' = 1/F

1/s' = 1/F - 1/3F

1/s' = (2/3)*(1/F)

S' = (3/2)*F

size of the image / size of the object = (3/2)/3 = 1/2 <<<_--answer

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