Determine the object distance for a convex lens (f =19.7 cm) that produces an image, 130.8 cm away on a screen.

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BlackTom AI · Accepted Answer

Starting with the given problem, we are to determine the object distance, do, for a convex lens with focal length f = 19.7 cm that forms an image on a screen at di = 130.8 cm.

First, recall the thin-lens equation in the common distance form: 1/f = 1/do + 1/di, where do is the object distance and di is the image distance both measured from the lens and taken as positive for real distances on the same side conventions we are using here.

Since the image is projected on a screen, the image is real, so di is a positive real distance of 130.8 cm, and the focal length f is 19.7 cm (positive for a convex lens).

Rearranging the lens equation to solve for do gives: 1/do = 1/f − 1/di, which leads to do = f * di / (di − f).

Plugging in the numbers: di − f = 130.8 cm − 19.7 cm = 111.1 cm, and f * di = 19.7 cm * 130.8 cm = 2576.76 cm^2.

Therefore, do = 2576.76 / 111.1 ≈ 23.18 cm, which rounds to 23.2 cm when expressed with appropriate significant figures.

A quick consistency check: since di (130.8 cm) is much larger than f (19.7 cm), the object distance being around 23 cm is reasonable for a convex lens producing a real image far from the lens. If you consider the alternative forms of the lens equation, you would still arrive at the same result after careful algebra.

In summary, the object distance is approximately 23.2 cm.

Physics 1 Hon - Bowles - p06/p07 P10.22 - Lesson 6 Exit Ticket

Determine the object distance for a convex lens (f =19.7 cm) that produces an image, 130.8 cm away on a screen.

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