8. A parallel beam of light falls normally on a thin lens with a focal length of $F=150$ cm. Behind the lens, 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 initial distance from the lens to the screen. (15 points)
Answer: 170 cm or 130 cm

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

![](https://cdn.mathpix.com/cropped/2024_05_06_84fc2054d2075e5d2c9fg-12.jpg?height=320&width=831&top_left_y=865&top_left_x=635)

From this, we can see that there are two possible scenarios: the screen can be moved away from the lens or moved closer to it. As a result, the initial distance from the lens to the screen:

$S_{1}=150+20=170 \mathrm{~cm} \quad\left(5\right.$ points) or $S_{2}=150-20=130 \mathrm{~cm}$ (5 points).