The famous Chinese magician Foo Ling Yu performs a classic magic trick using a concave mirror with a focal length of 1.6 m. Foo uses the mirror to produce an image of a light bulb that is the same size as the light bulb itself and is at the same location. Explain, in complete sentences, how Foo accomplishes this magic trick. Be specific about the location of the light bulb.
To accomplish the magic trick, Foo Ling Yu positions the light bulb at the focal point of the concave mirror. The focal point is located at a distance of 1.6 meters from the mirror's surface. By placing the light bulb exactly at this point, the light from the bulb will reflect off the mirror and form an image that is exactly the same size as the actual light bulb.
When an object is placed at the focal point of a concave mirror, the reflected rays of light become parallel to each other. These parallel rays then converge to a point, creating an image that is the same size as the object and located at the same position as the object itself. In this case, the light bulb forms an image that is the same size and shape, appearing to be in the same position as the actual light bulb. This creates the illusion that the light bulb has magically multiplied or duplicated itself.
In order to understand how Foo Ling Yu accomplishes the magic trick using a concave mirror, let's break down the process step by step:
1. Foo positions the concave mirror with a focal length of 1.6 m in such a way that its curved side is facing towards the object, which in this case is a light bulb.
2. The light bulb is placed at a specific location, and let's say it is positioned exactly at the focal point of the concave mirror. The focal point is the point where parallel rays of light converge after reflecting off the mirror.
3. When the light from the bulb strikes the reflective surface of the mirror, it reflects back towards the focal point. Since the light bulb is positioned at the focal point, the reflected rays of light will travel parallel to the optic axis.
4. These parallel rays continue beyond the mirror's surface and create an image of the light bulb. Since the light rays are parallel, they do not converge or diverge, resulting in an image that is the same size as the actual light bulb.
5. Moreover, the image is formed at the same location as the light bulb itself. This is possible because the object (light bulb) is positioned at the focal point, which is a special property of concave mirrors.
Therefore, by carefully positioning the light bulb at the focal point of the concave mirror, Foo Ling Yu is able to create a magic trick where the mirror produces an image of the light bulb that is the same size as the object and at the same location.