8. A parallel beam of light falls normally on a thin lens. Behind the lens, at a distance of $80 \mathrm{~cm}$ from it, there is a screen on which a circular spot of a certain diameter is visible. If the screen is moved 40 cm, a spot of the same diameter will again be visible on the screen. Determine the focal length of the lens.

## (15 points)
Answer: 100 cm or 60 cm

Solution. A diagram explaining the situation described in the problem (5 points):

![](https://cdn.mathpix.com/cropped/2024_05_06_84fc2054d2075e5d2c9fg-06.jpg?height=320&width=831&top_left_y=865&top_left_x=635)

From this, it is clear that there are two possible scenarios: the screen can be moved away from the lens or moved closer to it. As a result, the focal length of the lens $F_{1}=80+20=100$ cm (5 points). Or $F_{2}=80-20=60$ cm (5 points).

## Final Stage

2017-2018 academic year
## Tasks, answers, and evaluation criteria

9th grade

Variant II

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