The second stage is to draw rays to the observer point from each of the image points. We can also complete the third stage by joining the light rays from the mirror to the object points as follows:. You can see that the observer can see an image of the top of their head and an image of their feet. In order that the angle of incidence equals the angle of reflection, the normal line must sit exactly half-way between the top of the head and the observer point. We therefore don't need the top edge of the mirror to be higher than 50mm above the observer point.
In order that the angle of incidence equals the angle of reflection, the normal line must sit exactly half-way between the observation point and the feet. The observer is mm high and the mirror needs to be mm long and, yes, this is half the height. Not only that, but we can state that the bottom of the mirror needs to start at mm from the floor.
We can see that this still works for a very close distance to the mirror. What about at a very long distance apart? Since the person is cm tall, the vertical dimension of the mirror must be at least 90 cm. The lower edge of the mirror must be at a height that is half the distance between his feet and eyes. Since the eyes are located 6 cm from the top of his head which means it is at a height of cm from his feet, the lower edge of the mirror must be 87 cm from the ground.
Explanation : Understanding the solution requires an intermediate result using the law-of-reflection. When a ray of light is incident on a plane reflecting surface, the incident ray and the reflected ray will lie on the same plane.
One can define the angles of incidence and reflection as follows:. A Useful Result : Consider a situation where a light ray from an object gets reflected by a mirror and enters an eye, as illustrated in the figure below.
If the object and the eye are at the same distance from the mirror then the law of reflection implies that the point of incidence lie exactly midway between the object and the eye. Applying This Result To Our Problem : Now let us apply the above result to our problem in which a cm tall person stands in front of a mirror. The top of her head, her eyes and her feet, all lie along the same vertical line. The two objects we are going to consider are the 'top of her head' and 'her feet'.
These two objects lie at the same distance from the mirror as her eyes. Ben convinced his parents that it would be a waste of money to buy a mirror longer than 3 feet. The Phooled family has been fooled. Unfortunately, the 3-foot mirror can be mounted in the perfect position for Ben to view his entire image. Suzie, who is 4 feet tall, may only need 2 feet of mirror to view her image. Yet the two foot section which Suzie needs extends to positions on the wall below the 3 foot section which Ben needs.
Suzie's eyeball position is lower and thus she must sight at a lower position on the mirror in order to view her feet. Physics Tutorial. My Cart Subscription Selection. Student Extras. Why is an Image Formed? We Would Like to Suggest Why just read about it and when you could be interacting with it? Interact - that's exactly what you do when you use one of The Physics Classroom's Interactives.
We would like to suggest that you combine the reading of this page with the use of our Who Can See Who? You can find this in the Physics Interactives section of our website. The Who Can See Who? Interactive provides learners with an intensive mental workout in determining who can see who when looking int a plane mirror. Visit: Who Can See Who? See Answer The Phooled family has been fooled.
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