/*! 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 3 A hair dresser stands with her n... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 3

A hair dresser stands with her nose \(20 \mathrm{~cm}\) infront of a plane mirror for what distance must she focus her eyes in order to see her nose in the mirror? (a) \(40 \mathrm{~cm}\) (b) \(50 \mathrm{~cm}\) (c) \(30 \mathrm{~cm}\) (d) \(60 \mathrm{~cm}\)

Short Answer

Expert verified
She must focus her eyes on 40 cm.

Step by step solution

01

Understanding the Problem

The hairdresser is looking into a plane mirror, and we need to determine how far she must focus in order to see the reflection of her nose clearly.
02

Concept of Plane Mirror Reflection

In a plane mirror, the distance of the object from the mirror is equal to the distance of the image from the mirror. This means that if an object is 'd' cm in front of the mirror, the image will be 'd' cm behind the mirror.
03

Calculate the Image Distance

The distance of the hairdresser's nose from the mirror is given as 20 cm. Since the image of the nose is also 20 cm behind the mirror, the total distance she must focus is the sum of these distances.
04

Compute the Total Focusing Distance

So, the nose is 20 cm in front of the mirror, and its image is 20 cm behind the mirror. Therefore, the total distance she must focus on is the sum: \( 20 + 20 = 40 \) cm.

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 Distance
In the context of a plane mirror, the concept of image distance is quite straightforward. When you stand in front of a mirror, your reflection appears to be behind the mirror the same distance that you are in front of it. This is what we refer to as the image distance.
If an object like your nose is placed 20 cm in front of the mirror, then the image of your nose will also be 20 cm behind the mirror.
Thus, the image and object are spaced equally from the mirror.
  • This implies the image distance in a plane mirror equals the object distance from the mirror.
  • Understanding this concept helps us visually comprehend how reflections are formed in everyday mirrors.
  • Remember: image distance is always the same as the object distance in plane mirrors.
Focusing Distance
Focusing distance is crucial when dealing with reflections, especially in plane mirrors. It is the total distance your eyes need to focus to see a clear image of the object you're looking at in the mirror.
In our example, the hairdresser's nose is 20 cm from the mirror. Therefore, her reflection is also 20 cm behind the mirror.
Hence, the total focusing distance comprises both the distance to the mirror and the distance from the mirror to the reflection.
  • To compute the focusing distance, simply sum the object distance and the image distance.
  • This formula ensures you account for both the journey to the mirror and the journey to the image.
  • For the hairdresser, she must focus on: 20 cm (to the mirror) + 20 cm (from the mirror to the image) = 40 cm total.
Reflection Concepts
Reflection in a plane mirror revolves around some core concepts that make understanding easier.
A plane mirror reflects light in such a manner that the angle of incidence equals the angle of reflection.
This consistent rule forms the basis for how images appear in mirrors.
  • An image in a plane mirror is virtual, meaning it cannot be projected onto a screen because it seems to be located behind the mirror.
  • The size of the image is the same as the size of the object; images are neither magnified nor reduced.
  • This consistent behavior explains why plane mirrors are often used for everyday tasks like grooming.

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

Two plane mirrors are perpendicular to each other. A ray after suffering reflection from the two mirrors will be (a) perpendicular to the original ray (b) parallel to the original ray (c) parallel to the first mirror (d) at \(45^{\circ}\) to the original ray

Two plane mirrors are combined to each other as such one is in \(y-z\) plane and other is in \(x-z\) plane. A ray of light along vector \(\hat{i}+\hat{j}+k\) is incident on the first mirror. The unit vector in the direction of emergence ray after successive reflections through the mirror is: (a) \(-\frac{1}{\sqrt{3}} \hat{i}-\frac{1}{\sqrt{3}} \hat{j}+\frac{1}{\sqrt{3}}\) (w) \(-\frac{1}{\sqrt{3}} \hat{i}-\frac{1}{\sqrt{3}} \hat{j}-\frac{1}{\sqrt{3}}\) (c) \(-\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}\) (d) none of these

Two plane mirrors are inclined at an angle such that a ray incident on a mirror undergoes a total deviation of \(240^{\circ}\) after two reflections. The angle between mirrors. Also discuss the formation of image : (a) \(60^{\circ}, 5\) (b) \(5^{\circ}, 60\) (c) \(45^{\circ}, 5\) (d) \(30^{\circ}, 6\)

A man of height \(1.8 \mathrm{~m}\) stands infront of a large vertical plane mirror. The distance of the image from the man if he stands at a distance of \(1.5 \mathrm{~m}\) from the mirror is : (a) \(1 \mathrm{~m}\) (b) \(2 \mathrm{~m}\) (c) \(3 \mathrm{~m}\) (d) \(4 \mathrm{~m}\)

The position of \(1 \mathrm{~cm}\) tall object which is placed \(8 \mathrm{~cm}\) infront of a concave mirror of radius of curvature \(24 \mathrm{~cm}\) is: (a) \(24 \mathrm{~cm}\) (b) \(25 \mathrm{~cm}\) (c) \(26 \mathrm{~cm}\) (d) \(27 \mathrm{~cm}\)
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Magnetism

Read Explanation

Kinematics Physics

Read Explanation

Waves Physics

Read Explanation

Astrophysics

Read Explanation

Atoms and Radioactivity

Read Explanation
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.