Calculate the area of the patch of light reflected on the screen by a plane mirror

What is the area of the patch of light that is reflected on the screen?

The area of the patch of light that is reflected on the screen is 450 cm².

Explanation:

To find the area of the patch of light reflected on the screen, we can consider the geometry of the situation. Since the mirror and screen are parallel, the light rays from the source will be reflected at the same angle as they hit the mirror. This means that the angle of incidence is equal to the angle of reflection. Let's consider a ray of light that hits the mirror at point A and is reflected to point B on the screen. The distance between the mirror and the screen is 3m, and the source of light is located 1 meter from the mirror on the normal to its center. This forms a right-angled triangle with the mirror, screen, and the ray of light. Using the properties of similar triangles, we can determine the length of the reflected ray on the screen. The length of the mirror is 45 cm, and the distance between the mirror and the screen is 3m, which is equal to 300 cm. Therefore, the length of the reflected ray on the screen is (45/300) * 100 = 15 cm. The area of the patch of light reflected on the screen can be calculated by multiplying the length of the reflected ray by the width of the mirror. The width of the mirror is 30 cm. Therefore, the area of the patch of light reflected on the screen is 15 cm * 30 cm = 450 cm².
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