Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 16: Problem 2213

"Bhautik" runs towards a plane mirror with a speed of \(20 \mathrm{~ms}^{-1}\), what is the speed of his image ? (A) \(45 \mathrm{~ms}^{-1}\) (B) \(20 \mathrm{~ms}^{-1}\) (C) \(15 \mathrm{~ms}^{-1}\) (D) \(7.5 \mathrm{~ms}^{-1}\)

Short Answer

Expert verified
The speed of Bhautik's image in the plane mirror is \(20 \mathrm{~ms}^{-1}\). Therefore, the correct answer is (B) \(20 \mathrm{~ms}^{-1}\).

Step by step solution

01

Analyze the movement with respect to the mirror

When Bhautik is running towards the mirror, the distance between him and the mirror is decreasing at a rate of \(20 \mathrm{~ms}^{-1}\). As the plane mirror forms an image that has the same distance away from it as the object, the image will also move in the same direction as Bhautik.
02

Find the speed of the image in the mirror

Since we know that the distance between the object (Bhautik) and its image in the plane mirror are equal and they are moving towards each other in the same direction, the speed of the image will also be equal to the speed of Bhautik.
03

Write the final answer

The speed of Bhautik's image in the plane mirror is \(20 \mathrm{~ms}^{-1}\). Therefore, the correct answer is (B) \(20 \mathrm{~ms}^{-1}\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

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

Image Speed
When discussing plane mirrors, one interesting aspect is determining how fast the image of an object moves. This is what we call the "image speed". In the case of a plane mirror, the image speed is directly related to the speed of the object itself. This is because the image in a plane mirror mirrors all actions of the object almost perfectly, albeit in reverse.

If you are running towards the mirror at a speed of 20 meters per second, your image appears to move towards you at the same speed of 20 meters per second. An important aspect to note is that this is only true for plane mirrors, and not other reflective surfaces like concave or convex mirrors, which alter the size and distance ratios of the images they reflect due to their shapes.

In general:
  • The speed of the image equals the speed of the object.
  • The direction of image movement is opposite to the direction of object movement as perceived by someone looking at the mirror.
  • Understandably, for every movement made by the object, the mirror reflects it, keeping the image equidistant from the mirror at all times.
Mirror Reflection
The reflection process in a plane mirror is governed by the simple law of reflection: the angle of incidence is equal to the angle of reflection. What this means in simpler terms, is how light behaves when it hits the mirror. Light rays from the object hit the mirror and reflect back to our eyes, creating the visual perception of the image.

This reflection is responsible for forming images that appear behind the mirror at an equal distance to the object in front of the mirror. This creates the illusion of depth and distance. However, it's important to realize that no actual imagery exists behind the mirror; it's merely a perception formed by our eyes interpreting the reflected light.

In essence, reflection from plane mirrors results in images that are:
  • Virtual because they appear to be behind the mirror and cannot be projected onto a screen.
  • Upright, maintaining the same orientation as the object.
  • The same size as the object, which is not always the case with concave or convex mirrors.
  • Laterally inverted, meaning left is right and right is left in the reflection.
Relative Motion in Mirrors
Understanding relative motion in mirrors can be very intriguing. With mirrors, perception plays a huge role in how motion is perceived. In a situation with a moving object in front of a stationary mirror, like when "Bhautik" runs towards the mirror, the image moves as if it is also approaching bhautik at the same speed.

The concept of relative motion helps solve problems where both the object and image are considered to be moving simultaneously. From Bhautik's perspective, as he moves towards the mirror, his image appears to be moving towards him:

  • The speed of the image relative to Bhautik doubles because as the image moves towards him, the distance between Bhautik and his image decreases at twice the rate of his running speed.
  • This means the relative speed, from Bhautik's point of view, seems like 40 meters per second, even though both are actually moving at 20 meters per second.
Understanding these contrasts helps in grasping the real-world implications of physics in day-to-day activities involving mirrors.

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

\(\mathrm{n}^{\text {th }}\) bright fringe of red light \(\left(\lambda_{1}=7500 \AA\right.\) ) Coincides with \((\mathrm{n}+1)^{\text {th }}\) bright fringe of green light \(\left(\lambda_{2}=6000 \AA\right)\). The value of \(n=\) (A) 8 (B) 4 (C) 2 (D) 1

In a thin prism of glass \(\left(a_{(n) g}=1.5\right)\) which of the following relation between the angle of minimum deviation \(\delta_{\mathrm{m}}\) and the angle of refraction \(\mathrm{r}\) will be correct? (A) \(\delta_{\mathrm{m}}=(\mathrm{r} / 2)\) (B) \(\left(\delta_{\mathrm{m}} / 2\right)=\mathrm{r}\) (C) \(\delta_{\mathrm{m}}=1.5 \mathrm{r}\) (D) \(\delta_{\mathrm{m}}=\mathrm{r}\)

The phenomenon of polarization of electromagnetic waves proves that the electromagnetic waves are (A) mechanical (B) longitudinal (C) transverse (D) none of these

Read the paragraph and chose the correct answer of the following questions In young experiment position of bright fringes is given by \(\mathrm{x}=\mathrm{n} \lambda(\mathrm{D} / \mathrm{d})\) and the position of dark fringes is given by \(\mathrm{x}=(2 \mathrm{n}-1)(N 2)(\mathrm{D} / \mathrm{d})\) where \(\mathrm{n}=1,2,3 \ldots \ldots \ldots \ldots\) for first second, third bright/dark fringe. The center of the fringe pattern is bright (for \(\mathrm{n}=0\) ). The width of each bright/dark fringe is \(\beta=(\lambda \mathrm{D} / \mathrm{d})\), Where \(\lambda=5000 \AA\). Slits are \(0.2 \mathrm{~cm}\) apart and \(\mathrm{D}=1 \mathrm{~m}\) (i) If light of wavelength \(6000 \AA\) be used in the above experiment the fringe width would be \(\mathrm{mm}\) (A) \(0.30\) (B) 3 (C) \(0.6\) (D) 6 (ii) with the light of wavelength \(5000 \AA\), If experiment were carried out under water of a \(n=(4 / 3)\) the fringe width would be (A) zero (B) \((4 / 3)\) times (C) (3/4) times (D) none of these

Relation between critical angle of water \(C_{w}\) and that of the glass \(\mathrm{C}_{\mathrm{g}}\) is (given, \(\left.\mathrm{n}_{\mathrm{w}}=(4 / 3), \mathrm{n}_{\mathrm{g}}=1.5\right)\) (A) \(\mathrm{C}_{\mathrm{w}}<\mathrm{C}_{\mathrm{g}}\) (B) \(\mathrm{C}_{\mathrm{w}}=\mathrm{C}_{\mathrm{g}}\) (C) \(\mathrm{C}_{\mathrm{w}}>\mathrm{C}_{\mathrm{g}}\) (D) \(\mathrm{C}_{\mathrm{w}}=\mathrm{C}_{\mathrm{g}}=\mathrm{O}\)
See all solutions

Recommended explanations on English Textbooks

Text Comparison

Read Explanation

History of English Language

Read Explanation

Phonetics

Read Explanation

Language Analysis

Read Explanation

Email

Read Explanation

Creative Story

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.

Sign-up for free