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If two adjacent walls and the ceiling of a rectangular room are mirror surfaced, then how many images of himself, a man can see? (a) 3 (b) 5 (c) 6 (d) 9

Short Answer

Expert verified
(c) 6 images.

Step by step solution

01

Identify Surfaces That Reflect

Visualize the room as having four walls, a ceiling, and a floor. In this problem, two adjacent walls and the ceiling act as mirrors. This means any object, like a person, will see images created by reflections from these three surfaces.
02

Determine Reflections From Each Wall

Start by considering the reflections in each single mirror surface. The person will see one image per mirror, leading to a basic count of three initial images: one from each wall (left and right) and one from the ceiling.
03

Consider Double Reflections

Next, consider the reflections seen in two mirrors simultaneously, a phenomenon known as double reflections. These occur where the lines of intersection between the mirrors exist. Considering two adjacent walls and the ceiling, assess that a double reflection creates an additional image per pair of mirrors.
04

Include Triple Reflections

Now think about when all three surfaces reflect light simultaneously. This happens in the corner where two walls meet the ceiling, causing one additional image due to the combined triple reflection.
05

Calculate Total Number of Images

Add together the basic reflections (3 images), the double reflections (3 additional images), and the triple reflection (1 image). This results in a total of 7 images visible to the person.

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Key Concepts

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

Mirror Physics
The fascinating world of mirror physics centers around understanding how reflective surfaces can manipulate light to create images. Mirrors work by reflecting light rays, allowing us to see reflections of objects. When light hits a mirror, it bounces back at an angle equal to the angle at which it arrived, in a process called reflection. Here, two adjacent walls and the ceiling function as mirrors.
This alters the room's perception by adding virtual images of a man standing in it. These images depend on the positions and orientations of the mirrors. In the given problem, these three surfaces multiply reflections, producing multiple images, interestingly explained by combining basic and complex reflections.
Mirror physics is essential for understanding more complicated optical systems, beyond simple reflections.
Optics in Physics
Optics, the study of light, is an important part of physics that helps us understand phenomena like image formation and reflection patterns. Reflections, as explored in mirror physics, are just a small part of optics.
The field involves understanding how light travels and how it's affected by different materials, like mirrors. Optics reveals how light behaves when it moves through spaces and reflects off surfaces, thus showing how mirrors can create multiple images. It also introduces principles like the angle of incidence equaling the angle of reflection, which is key for predicting mirror reflections.
Knowing these principles helps explain the complex interplay of light in this mirrored room, leading to the images seen.
Image Formation
In optics, image formation is a key concept explaining how mirrors and lenses create multiple sightings of an object. An image is formed when light rays reflect and meet or appear to meet at a point. In the mirrored room scenario, each wall and the ceiling forms an image of the man standing inside.
Initially, each mirror forms a primary image from direct light reflection.
  • Every ray bouncing off the wall shows an image reflected from that mirror.
  • Further images come from double and triple reflections, where light interacts with multiple surfaces before coming to the viewer.
These layered reflections culminate in secondary and tertiary images, revealing reflections would be more in number given the room's geometry and reflective surfaces.
Understanding image formation in mirrors is fundamental to mastering reflections.
Reflection Patterns
Reflection patterns explain how images are systematically formed based on multiple reflections in a room with mirrored surfaces. The exercise demonstrates distinct patterns based on how light reflects off each surface:
- **Single Reflection**: This occurs when light bounces off one mirror surface, forming basic images.
- **Double Reflection**: This is when light captures reflections off two mirrors, usually seen where walls meet.
- **Triple Reflection**: Occurring where walls and ceiling converge, forming an additional image.
Each pattern causes different image appearances. Understanding these patterns enables prediction of how many images will form, as light traverses complex paths amidst the reflective surfaces.
Such reflection patterns explain why in this scenario a person can see a sum of seven images due to combined reflection effects.

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Most popular questions from this chapter

If two mirrors are inclined at some angle and an object is placed between the mirrors and there are 7 images formed for an object. Then what is angle between the mirrors? (a) \(54^{\circ}\) (b) \(50^{\circ}\) (c) \(60^{\circ}\) (d) \(64^{\circ}\)

Two plane mirrors are placed parallel to each other. A. point object is placed between them. The distance of image formed in one of the mirror is in :(a) harmonic progression (b) arithmetic progression (c) geometric progression (d) both harmonic and arithmetic progression

A mirror is inclined at an angle of \(\theta\) with the horizontal. If a ray of light is incident at an angle of incidence \(\theta\), then the reflected ray makes the following angle with horizontal: (a) \(\theta\) (b) \(2 \theta\) (c) \(\theta / 2\) (d) none of these

An object of height \(5 \mathrm{~cm}\) is placed in midway between a concave mirror of radius of curvature \(30 \mathrm{~cm}\) and a convex mirror of radius of curvature \(30 \mathrm{~cm}\). The mirrors are placed opposite to each other and are \(60 \mathrm{~cm}\) apart. The position of the image formed by reflection at convex mirror is : (a) \(10 \mathrm{~cm}\) (b) \(20 \mathrm{~cm}\) (c) \(15 \mathrm{~cm}\) (d) \(13 \mathrm{~cm}\)

A ray is incident on a plane surface. If \(\hat{i}+\hat{j}-\hat{k}\) represents a vector along the direction of incident ray. \(\hat{i}+\hat{j}\) is a vector along normal on incident point in the plane of incident and reflected ray. Then vector along the direction of reflected ray is: (a) \(-\frac{1}{\sqrt{19}}(-3 \hat{\mathbf{i}}+3 \hat{j}+\mathbf{k})\) (b) \(\frac{1}{\sqrt{19}}(3 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\cdot \hat{\mathrm{k}})\) (c) \(-\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})\) (d) \(\hat{\mathbf{k}}\)

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