The optical principle of the pinhole camera is used in various equipment, such as video projectors, slide projectors, cameras, and television cameras, among others. Which of these devices requires a converging lens to create the image?

The main characteristics of the camera obscura are: its shaded internal walls, which do not allow any external light to enter, and its opening, which allows only a small amount of light from the projected object to enter. Therefore, based on the optical principle of the camera obscura, why is it necessary for the internal walls to be shaded?

A dark chamber is a device that demonstrates the principle of image formation and is a prototype of the first photographic cameras. Consider a dark chamber that has a small opening in the shape of a 2 mm diameter circle on one side. On the opposite side of the opening, 40 cm away, there is a sheet of paper. A luminous object is placed 5 meters from the opening. Based on the Huygens-Fresnel principle, calculate the size of the image formed on the sheet of paper. Consider light as propagating in a straight line and neglect any diffraction or dispersion effects of light in the calculation. Describe the formation of the image step by step, considering the path of light from the object to the sheet of paper, and explain how the size of the opening affects the sharpness of the image formed.

To watch his team's games, Gil bought a state-of-the-art projector and intends to set it up in a room in his house with a white wall. According to the manufacturer's information, for the image to be perfect, the device must be set up in such a way that the point where the lens through which the light comes out is positioned as the vertex of a right pyramid with the rectangular image formed on the wall as the base. Following this guidance, Gil set up the device two meters away from the wall and observed that the projected image forms a rectangle with an area of 6 square meters. If he moves the projector to three meters away from the wall, the area of the formed image will be

To solve this question, let's consider that the image projected on the wall forms a similarity of triangles, as the projector's lens is the vertex of a right pyramid and the base is the rectangular image formed on the wall. When Gil moves the projector backwards, increasing the distance from the wall, the base of the pyramid (the projected image) also increases proportionally. Let's follow the steps: 1. Initially, the projector is 2 meters away from the wall and the area of the image is 6 square meters. The area of a rectangle is given by A = length × width. 2. When Gil moves the projector to 3 meters away, the new distance is 1.5 times larger than the original distance (3 meters / 2 meters = 1.5). Due to proportionality, both the length and width of the new projected image will also be 1.5 times larger than the original dimensions. 3. Let L be the length and W be the width of the original image. Then, the original area is A = L × W = 6 square meters. 4. The new dimensions of the image will be 1.5L and 1.5W, as both dimensions increase in the same proportion as the distance from the projector to the wall. 5. The new area of the image will be A' = (1.5L) × (1.5W) = 1.5^2 × (L × W) = 1.5^2 × 6 square meters, as the area is proportional to the square of the linear dimensions. 6. We calculate the new area: A' = 2.25 × 6 square meters = 13.5 square meters. Therefore, the area of the image formed when the projector is moved to three meters away from the wall will be 13.5 square meters, which corresponds to option (c).

In "The light that passes through a small opening." (line 1), the term "light" is classified as:

Question bank: Geometric Optics: Camera Obscura

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