/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 2 (1) Suppose that you want to tak... [FREE SOLUTION] | 91Ó°ÊÓ

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(1) Suppose that you want to take a photograph of yourself as you look at your image in a mirror 2.8 \(\mathrm{m}\) away. For what distance should the camera lens be focused?

Short Answer

Expert verified
Focus the camera at 5.6 meters.

Step by step solution

01

Understand the Problem

To solve this problem, we need to determine the distance at which the camera should be set to focus when taking a photo of your image in a mirror. The key idea here is using the law of reflection to find out how far the 'image' is from the camera.
02

Identify Key Information

The distance between you (the object) and the mirror is 2.8 meters. By the law of reflection, the distance from the mirror to your image is the same as the distance from you to the mirror, which is also 2.8 meters. Thus, your image appears to be behind the mirror.
03

Determine Total Distance

The distance from yourself to your image in the mirror is the sum of the distance from you to the mirror and the distance from the mirror to your image. This is calculated as: \[2.8 \, ext{m} + 2.8 \, ext{m} = 5.6 \, ext{m}\]
04

Conclusion on Camera Focus

The camera should be focused at a distance of 5.6 meters, which is the total distance from you to your image as perceived in the mirror.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Law of Reflection
The "Law of Reflection" is a fundamental concept in physics, especially when dealing with light and mirrors. It states that when a ray of light strikes a smooth surface, it reflects off the surface in such a way that the angle it hits the surface, called the angle of incidence, is equal to the angle at which it reflects away, called the angle of reflection. This can be summarized as:
\[\text{Angle of incidence} = \text{Angle of reflection}\]
  • Angle of Incidence: The angle formed between the incoming ray and the normal (an imaginary line perpendicular to the surface) at the point of contact.
  • Angle of Reflection: The angle formed between the reflected ray and the normal at the point of reflection.
This principle applies to all smooth surfaces that reflect light, such as mirrors. In the context of the exercise, it's crucial to understand that this law helps us determine how the image forms a specific distance behind the mirror.
Image Distance
Image distance refers to the distance from the mirror to the point where the image is formed behind it, as seen by an observer. When you are standing in front of a mirror, the image does not actually exist behind the mirror, but appears to be at that point due to reflection. This calculated image distance is crucial for photographers to focus correctly, especially when capturing images in mirrors.
The exercise demonstrates this concept by showing that the image of an object at a distance of 2.8 meters from a mirror appears to be an equal distance behind the mirror. Thus, the total distance from the object to its image is the sum of the object-to-mirror distance and the mirror-to-image distance, which in this case is:
\[2.8 \text{ m} + 2.8 \text{ m} = 5.6 \text{ m}\]Understanding image distance is crucial for tasks like focusing a camera, as failing to calculate the correct depth can lead to blurry or unfocused images.
Mirror Reflection
"Mirror Reflection" is the phenomenon where light bounces off a reflective surface, such as a mirror, obeying the law of reflection. This process creates an image that our eyes perceive as being behind the mirror. In a flat mirror (plane mirror), the image formed is:
  • Virtual: The image cannot be projected onto a screen as it's not formed by actual convergence of rays.
  • Upright: The image maintains the orientation of the object.
  • Laterally inverted: The left and right sides are reversed in the image relative to the object.
  • Same Size: The image is of the same size as the object.
In the context of photographing your reflection in a mirror, these characteristics are essential to predict how the image would appear in the photograph. By understanding mirror reflection, one can better gauge the distance for focusing the camera and ensure the captured image reflects reality accurately.

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Most popular questions from this chapter

A light beam coming from an underwater spotlight exits the water at an angle of \(56.0^{\circ} .\) At what angle of incidence did it hit the air-water interface from below the surface?

(II) Show that if two plane mirrors meet at an angle \(\phi,\) a single ray reflected successively from both mirrors is deflected through an angle of 2\(\phi\) independent of the incident angle. Assume \(\phi<90^{\circ}\) and that only two reflections, one from each mirror, take place.

A ray of light, after entering a light fiber, reflects at an angle of \(14.5^{\circ}\) with the long axis of the fiber, as in Fig. \(32-56 .\) Calculate the distance along the axis of the fiber that the light ray travels between successive reflections off the sides of the fiber. Assume that the fiber has an index of refraction of 1.55 and is \(1.40 \times 10^{-4} \mathrm{~m}\) in diameter.

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(I) How far from a concave mirror (radius 24.0 \(\mathrm{cm}\) ) must an object be placed if its image is to be at infinity

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