6. (4 points) Behind a thin converging lens with a focal length $F$ and diameter $D$, a flat screen is placed perpendicular to its optical axis at its focus. In front of the lens on the main optical axis, at a distance $d > F$ from the lens, a point light source is placed. Determine the diameter of the light spot on the screen.

Possible solution. Consider the diagram. From the diagram, using the similarity of triangles formed by the ray and the main and secondary axes, it is clear that

$$
D^{\prime}=\frac{F D}{d}
$$
Answer: $D^{\prime}=\frac{F D}{d}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_c1ac34e9a4408671a8e0g-05.jpg?height=417&width=491&top_left_y=2266&top_left_x=1436)

## Grading Criteria

| Performance | Score |
| :--- | :---: |
| The participant did not start the task or performed it incorrectly from the beginning | $\mathbf{0}$ |
| The drawing is constructed | $\mathbf{1}$ |
| Similar triangles are considered | $\mathbf{2}$ |
| Necessary transformations are performed and the answer is obtained | $\mathbf{1}$ |
| Total points | $\mathbf{4}$ |

10th grade

## Variant 2