Física entretenida - El enigma de los espejos

Key Concepts:

• Espejo de cuerpo entero (Full-length mirror)
• Largo mínimo del espejo (Minimum mirror length)
• Altura (Height)
• Ley de la reflexión (Law of reflection)
• Ángulo de incidencia (Angle of incidence)
• Ángulo de reflexión (Angle of reflection)

Experiment Setup and Measurements:

The experiment aims to determine the minimum length of a mirror required to see one's entire body. The materials used include a mirror, a measuring tape (wincha), adhesive tape, and a helper. The subject must be centered in the mirror to see a full-body reflection.

1. Height Measurement: The subject's height is measured using a set square (escuadra) and measuring tape. The subject's height is determined to be 1 meter and 87 centimeters (1.87 m).
2. Mirror Marking: The helper marks two points on the mirror: the lower point corresponding to the bottom of the subject's feet in the reflection and the upper point corresponding to the top of the subject's head in the reflection.
3. Distance Measurement on Mirror: The distance between the two marks on the mirror is measured using the measuring tape. The measured distance is 93.5 cm.

Results and Conclusion:

The distance between the marks on the mirror (93.5 cm) is exactly half of the subject's height (1.87 m). Therefore, the minimum length of the mirror required to see a full-body reflection is half of the person's height.

Key Argument and Supporting Evidence:

The main argument is that the minimum mirror length should be half the person's height to see a full reflection. The experiment provides empirical evidence supporting this claim by directly measuring the required length on the mirror and comparing it to the subject's height.

Distance Independence:

The experiment emphasizes that the required mirror length is independent of the distance between the person and the mirror. Whether the person stands 1 meter, 2 meters, 5 meters, or even 1 kilometer away from the mirror, the distance between the marks on the mirror (representing the minimum required length) remains constant at half the person's height.

Explanation Based on the Law of Reflection:

The experiment's outcome is explained by the law of reflection, which states that the angle of incidence is equal to the angle of reflection. This principle dictates how light rays from the top and bottom of the person's body reflect off the mirror and reach the observer's eyes, determining the minimum mirror size needed for a full-body view.

Notable Quotes:

• "¿Cuál es la conclusión? La conclusión es muy sencilla: el largo mínimo del espejo debe ser igual a la mitad de la longitud de mi cuerpo si queremos vernos completos, es decir, desde el extremo de mi cabeza hasta el extremo de mis pies." (What is the conclusion? The conclusion is very simple: the minimum length of the mirror must be equal to half the length of my body if we want to see ourselves completely, that is, from the end of my head to the end of my feet.)
• "Es muy importante tomar en cuenta el hecho de que estas marcas que hemos realizado en el espejo son independientes de la distancia a la cual nos encontremos del espejo." (It is very important to take into account the fact that these marks that we have made on the mirror are independent of the distance at which we are from the mirror.)

Synthesis/Conclusion:

The video demonstrates through a simple experiment that the minimum length of a mirror required to see a full-body reflection is half of the person's height. This conclusion is supported by empirical measurements and explained by the fundamental law of reflection. The required mirror length is independent of the distance between the person and the mirror.