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Ch 34: Ray Optics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 34: Ray OpticsProblema 46
Capitolo 34, Problema 46

The place you get your hair cut has two nearly parallel mirrors 5.0 m apart. As you sit in the chair, your head is 2.0 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be? Neglect the thickness of your head.

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1
Understand the problem: The two mirrors are parallel and separated by a distance of 5.0 m. Your head is 2.0 m from the nearer mirror. The problem involves multiple reflections between the mirrors, and we need to determine the apparent distance of the back of your head as seen in the reflections.
Step 1: Calculate the distance of the first reflection of your head in the nearer mirror. Since your head is 2.0 m from the nearer mirror, the first image will appear 2.0 m behind this mirror. This means the first image is at a distance of 2.0 m + 2.0 m = 4.0 m from your head.
Step 2: Determine the position of the first reflection in the farther mirror. The first image in the nearer mirror acts as a virtual object for the farther mirror. The distance of this virtual object from the farther mirror is the separation between the mirrors (5.0 m) plus the distance of the first image behind the nearer mirror (2.0 m), giving a total of 5.0 m + 2.0 m = 7.0 m. The first reflection in the farther mirror will appear 7.0 m behind it.
Step 3: Continue the process for subsequent reflections. Each reflection alternates between the two mirrors, with the distance increasing by twice the separation of the mirrors (2 × 5.0 m = 10.0 m) for each additional reflection. For example, the second reflection in the nearer mirror will appear 7.0 m + 10.0 m = 17.0 m behind it, and so on.
Step 4: Identify the reflection corresponding to the back of your head. The back of your head appears in the second reflection in the nearer mirror. This is because the light travels from the back of your head to the farther mirror, reflects back to the nearer mirror, and then reaches your eyes. The apparent distance of this reflection is 17.0 m from your head.

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Reflection of Light

Reflection of light occurs when light rays bounce off a surface, such as a mirror. The angle of incidence, which is the angle between the incoming ray and the normal (a perpendicular line to the surface), equals the angle of reflection. This principle allows us to see images in mirrors, as light reflects off the surface and travels to our eyes, creating the perception of depth and distance.
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Law of Reflection

Virtual Images

A virtual image is formed when light rays appear to diverge from a point behind a mirror, rather than converging at that point. In the case of parallel mirrors, the virtual images of objects can appear at various distances depending on the position of the object relative to the mirrors. This concept is crucial for understanding how the back of your head is perceived when looking into the mirrors.
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Example 1

Distance Calculation in Mirror Systems

In a system with two parallel mirrors, the distance to the virtual image can be calculated by considering the distances from the object to each mirror. The total distance to the virtual image is effectively double the distance from the object to the nearest mirror, as the light reflects back and forth between the mirrors. This principle helps determine how far away the back of your head appears when viewed in the mirrors.
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Mirror Equation
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