An object initially at infinity is brought closer to the focus of a concave mirror. As the object moves in, (A) the inverted image moves closer to the focus and becomes larger. (B) the inverted image moves farther out from the focus and becomes larger. (C) the upright image moves closer to the focus and becomes larger. (D) the upright image gets farther out from the focus and becomes larger. (E) the inverted image gets farther from the focus and becomes smaller.

Short Answer

Expert verified
As the object moves closer to the focus in a concave mirror, the inverted image moves farther out from the focus and becomes larger.

Step by step solution

01

Understand concave mirrors and types of images they form

A concave mirror is a spherical mirror with the reflective surface facing inwards. The light rays converge at the focal point of the mirror, which is at a distance of half the radius of curvature (f = R/2) from the mirror. When an object is placed at different positions relative to the mirror's focus, the image formed can be of different types such as real or virtual and can have different magnifications. It is important to identify which of these types of images are formed as the position of the object changes.
02

Identify the movement and image properties when the object is at various distances from the mirror

The following are the cases regarding the position of the object relative to a concave mirror and the corresponding image properties: 1. Object at infinity: The image formed is real, inverted and diminished, located at the focus. 2. Object beyond the center of curvature (C): The image is real, inverted, and has a magnification less than 1. It is located between the focus (F) and the center of curvature (C). 3. Object at the center of curvature (C): The image is real, inverted, and has a magnification equal to 1. It is also located at the center of curvature (C). 4. Object between focus (F) and center of curvature (C): The image is real, inverted, and has a magnification greater than 1. It is located beyond the center of curvature (C). 5. Object at the focus (F): No real image is formed in this case. 6. Object between the mirror and focus (F): The image is virtual, upright, and magnified. It is formed behind the mirror. Now that we have this information, we can use it to determine which of the answer options is correct.
03

Analyze the answer choices and select the correct one

Based on our understanding of concave mirrors, we can now rule out the options which involve an upright image (C and D), since the object is never between the mirror and the focus, which is the only case that produces an upright image. Analyzing the remaining options: (A) As the object moves in from infinity, the image initially starts at the focus and moves further from it (beyond the focus, between F and C). Therefore, option (A) is incorrect. (B) As the object moves closer to the mirror, the real and inverted image moves farther out from the focus and becomes larger. This is in line with the properties we discussed in step 2. Therefore, this answer choice is correct. (E) The inverted image does not move farther from the focus and become smaller as the object moves closer. This is the opposite of what happens in the case of concave mirrors. Hence, option (E) is incorrect. The correct answer is (B) the inverted image moves farther out from the focus and becomes larger.

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Key Concepts

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

SAT Physics Preparation
Preparing for the SAT Physics subject test requires a solid understanding of key concepts in optics, particularly the behaviors of mirrors and lenses. Concave mirrors are a frequent topic due to their unique image formation properties.

For SAT physics preparation, focus on the nature of concave mirrors: how they reflect light to form images and how changing the object distance alters image characteristics like size, orientation, and type (real or virtual). It's crucial to understand how an object moving from infinity towards the focal point of a concave mirror produces a real, inverted image that increases in size. This understanding directly applies to multiple-choice questions, where you often analyze scenarios to determine image properties.
AP Physics Review
For students reviewing AP Physics, concave mirrors are part of the broader topic of optics. Optics is essential in the AP curriculum, encompassing reflection, refraction, and the behavior of light.

In the context of AP physics review, dive deep into ray diagrams for concave mirrors, an important technique for visualizing image formation. Ray diagrams help in predicting where an image will appear, how large it will be, and whether it's real or virtual. Remember that a real image can be projected on a screen, inverted, and is formed when light rays actually converge, while a virtual image is upright and cannot be projected as it results from diverging rays appearing to converge behind the mirror.

Lastly, grasp the impact of varying object distances on image properties by referring to the mirror equation \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \) and magnification formula \( m = -\frac{d_i}{d_o} \) where \(f\text{ is the focal length, }d_o\text{ is the object distance, and }d_i\text{ is the image distance.\)}
Optics and Light
Optics is a segment of physics that explores the behavior of light and its interactions with substances, including reflection, which is the phenomena of light bouncing off surfaces. Concave mirrors, with their inwardly curved reflective surfaces, are a classic example of this interaction.

Understanding how light rays converge at the focal point of a concave mirror is fundamental to mastering optics. Ray diagrams can be especially helpful to visualize this. When light rays parallel to the principal axis of a concave mirror reflect, they converge at the focal point. The position of the object relative to the mirror's focal point determines the nature of the image formed - whether it is diminished, has the same size, or is magnified and whether it is real or virtual.
Image Formation
Image formation by concave mirrors is a captivating application of optics. The type of image formed—real or virtual—depends on the object's position in relation to the mirror's focal point.

Close to the focal point, images are virtual, upright, and enlarged, as seen in makeup mirrors. At the focal point, theoretically, no image forms as rays parallel to the principal axis reflect and meet at the focal point. By moving an object from infinity towards the mirror, the image transitions from a small, diminished point at the focal point to larger and further away from the mirror beyond the focal point.

The subtle details of image formation with concave mirrors require attention to conceptual clarity. Exercises involving moving objects and predicting image characteristics enhance your understanding and are vital practice for both classroom and standardized exams.

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Most popular questions from this chapter

A beam of parallel light rays is incident on the same screen in the previous problem. If you want to produce a diffraction pattern on the distant wall, you should place in the clamps which of the following optical devices? (A) A prism (B) A narrow slit in a piece of cardboard (C) A rectangular piece of glass (D) A converging lens (E) A diverging lens

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An object is placed outside the focus of a diverging lens, as shown below. The image produced is (A) virtual, upright, on the object side of the lens (B) virtual, upright, on the opposite side of the lens from the object (C) virtual, inverted, on the opposite side of the lens from the object (D) real, inverted, on the object side of the lens (E) no image is formed

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