/*! 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 62 An object is placed between two ... [FREE SOLUTION] | 91影视

91影视

An object is placed between two plane mirrors arranged at right angles to each other at a distance \(d_{1}\) from the surface of one mirror and a distance \(d_{2}\) from the other. (a) How many images are formed? Show the location of the images in a diagram. (b) Draw the paths of rays from the object to the eye of an observer.

Short Answer

Expert verified
Three images are formed. Images appear due to reflections on each mirror, with ray paths head towards the observer.

Step by step solution

01

Count Images Formed by Mirrors

When two plane mirrors are arranged at right angles (90 degrees), they form multiple images. The number of images ( ) formed can be calculated by the formula =180/胃 - 1. Here, 胃 is the angle between the mirrors. For right-angle mirrors (胃=90), =180/90 - 1 = 2. Thus, there will be three images formed by the mirrors, including the mirror reflections.
02

Draw Diagram of Image Locations

To show the location of images, place the object at the intersection of the two mirrors with distances d鈧 and d鈧 from each mirror. Image I1 is formed as if the mirror at distance d鈧 is a single mirror reflecting the object. Image I2 is formed by the reflection from the mirror at distance d鈧, acting alone. Image I3 is a result of double reflection, first off the mirror at d鈧 and then off the mirror at d鈧. Place I1 symmetrically across the d鈧 mirror and I2 across the d鈧 mirror. I3 will appear as if I1 is reflected again in the d鈧 mirror.
03

Trace Ray Paths to Observer

To trace the path of rays from the object to an observer's eye, start by drawing lines (ray paths) from each image to where the observer would stand. For example, draw lines from Images I1, I2, and I3 to the observer. Extend these back towards the object through virtual paths on each mirror surface. When viewed by an observer, these appear as if they emanate from the images, giving the illusion that the images are located at the positions you marked in Step 2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Image Formation
When we talk about image formation in the context of plane mirrors, we are referring to the creation of virtual images that appear to exist at particular positions despite nothing being physically present there. This is a staple concept in optics.In the case of two plane mirrors placed at right angles, a unique phenomenon occurs. Each mirror reflects the object, creating an image. However, due to the 90-degree angle, the intersection of light paths allows for additional reflections, effectively multiplying the images.
  • Each mirror creates its primary image.
  • Further reflections occur between the two mirrors, producing additional images.
  • The images are located symmetrically with respect to the axis of the mirrors.
For two mirrors placed at right angles, we calculate the number of images formed using the formula: \(n = \frac{360}{\Theta} - 1\), where \(\Theta\) is the angle between the mirrors. This results in three images when the angle is 90 degrees. Understanding this principle helps us delve into how light behaves in geometrical optics.
Reflection
Reflection is the process where light bounces off a surface. With plane mirrors, this process adheres to a specific rule called the "law of reflection," which states that the angle of incidence is equal to the angle of reflection. When light hits a mirror, it reflects off the surface at an angle equal to the angle at which it arrived. This fundamental principle allows us to predict the behavior of light as it interacts with reflective surfaces.
  • Light travels in straight lines until it meets a surface.
  • It is this interaction鈥攔eflection鈥攖hat causes the formation of images.
  • Reflection in plane mirrors always results in virtual images, meaning the images cannot be projected onto a screen as they appear to be inside or behind the mirror.
In the exercise, the process of reflection creates images at different positions determined by the object's distance from each mirror. Such understanding of reflection is crucial when tracing ray diagrams or determining the locations of images in optical exercises.
Ray Diagrams
Ray diagrams are graphical representations illustrating how light rays interact with surfaces, such as mirrors, to form images. They are invaluable tools in optics for understanding and predicting image formation. In the context of our exercise, ray diagrams help visualize how three images are formed when light reflects between two plane mirrors arranged at right angles.
  • Draw the object and mirrors, positioning them correctly.
  • Show the pathway of light rays from the object to each mirror.
  • Extend the rays that reflect off the mirrors to trace where they appear to converge, forming virtual images.
Each image results from one or two reflections, as traced in the ray diagram. For example, Image I1 is depicted as light reflecting once off one mirror, while Image I3 involves light reflecting off both mirrors in succession. By using ray diagrams effectively, we can predict not only the existence of images but also their locations relative to the object. This makes ray diagrams a powerful visualization tool in geometric optics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A speck of dirt is embedded 3.50 \(\mathrm{cm}\) below the surface of a sheet of ice \((n=1.309) .\) What is its apparent depth when viewed at normal incidence?

When an object is placed at the proper distance to the left of a converging lens, the image is focused on a screen 30.0 \(\mathrm{cm}\) to the right of the lens. A diverging lens is now placed 15.0 \(\mathrm{cm}\) to the right of the converging lens, and it is found that the screen must be moved 19.2 \(\mathrm{cm}\) farther to the right to obtain a sharp image. What is the focal length of the diverging lens?

A glass plate 3.50 \(\mathrm{cm}\) thick, with an index of refraction of 1.55 and plane parallel faces, is held with its faces horizontal and its lower face 6.00 \(\mathrm{cm}\) above a printed page. Find the position of the image of the page formed by rays making a small angle with the normal to the plate.

A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall 6.00 \(\mathrm{m}\) to the right of the slide. The image is 80.0 times the size of the slide. (a) How far is the slide from the lens? (b) Is the image erect or inverted? (c) What is the focal length of the lens? (d) Is the lens converging or diverging?

A microscope is focused on the upper surface of a glass plate. A second plate is then placed over the first. To focus on the bottom surface of the second plate, the microscope must be raised 0.780 \(\mathrm{mm}\) . To focus on the upper surface, it must be raised another 2.50 \(\mathrm{mm}\) . Find the index of refraction of the second plate.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.