Question bank: Geometric Optics: Camera Obscura

A photography student decided to build his own darkroom to observe the behavior of light and image formation. For this, he used a box with a small hole on one of the faces and placed a translucent paper on the opposite side of the hole. On a sunny day, he positioned the darkroom facing a 6-meter tall tree 10 meters away. In the image formed on the translucent paper, the tree appeared with a height of 15 cm. (a) Calculate the distance between the hole and the translucent paper inside the darkroom. (b) If the student wishes to form an image of the tree on the translucent paper with twice the size of the current image (30 cm in height), what should he change: the distance from the darkroom to the tree or the distance from the hole to the translucent paper? Justify. (c) Calculate the new distance, according to the answer in item (b).

A dark chamber is a device that consists of a dark box with a small hole on one of its faces. When light enters through the opening, the outside image is projected onto the surface opposite the opening. Consider a rectangular dark chamber with a square hole of 1 cm on one of the smaller faces. A luminous object located 5 cm from the hole projects a sharp image on the opposite face. Using the principles of geometric optics, determine the distance between the object and the projected image. (Consider that light rays propagate in a straight line and that the focal distance of the system is 5 cm).

You have been tasked with conducting an experiment on a pinhole camera to present at the school's science fair. To do this, you decide to build a simple pinhole camera using a cardboard box, where a small hole on the side allows light to enter and form an image on the wall opposite the hole. Your camera has the following dimensions: 30 cm width, 40 cm height, and 50 cm length. An object is placed 2 meters away from the camera and has a height of 24 cm. Suppose the image is formed at the back of the box. a) Calculate the height of the image projected on the back of the camera using the proportion between the distances; b) Determine the necessary space between the pinhole and the opposite wall for the image to be in focus; c) Describe the procedure you would follow to conduct the experiment, considering the positioning of the camera, the object, and the lighting conditions.

A group of students decides to create a pinhole camera using a large cardboard box and a hole made on the side of the box, with the aim of projecting the image of a building that is 25 meters away. They observe that the projected image of the building inside the pinhole camera has a height of 10 cm. Knowing that the actual height of the building is 20 meters: 1) Calculate the distance from the hole to the bottom of the box (focal distance) to project this image with the mentioned height. 2) If the students decide to increase the size of the projected image to 15 cm in height, maintaining the same distance between the pinhole camera and the building, what should be the new focal distance of the camera? 3) Communicate the results obtained clearly and in detail and relate them to the physical principles behind the pinhole camera and its calculations.