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Chapter 19: Problem 7

A car is moving towards a plane mirror at a speed of \(30 \mathrm{~m} / \mathrm{s}\). Then the relative speed of its image with respect to the car will be : (a) \(30 \mathrm{~m} / \mathrm{s}\) (b) \(60 \mathrm{~m} / \mathrm{s}\) (c) \(15 \mathrm{~m} / \mathrm{s}\) (d) \(45 \mathrm{~m} / \mathrm{s}\)

Short Answer

Expert verified
The relative speed is \(60 \mathrm{~m/s}\), option (b).

Step by step solution

01

Understand the Problem

We're asked to find the relative speed of the image of a car with respect to the car itself, using the speed of the car and how planar mirrors create images.
02

Define the Concept for Plane Mirror Images

In a plane mirror, the image of an object is formed at the same distance behind the mirror as the object is in front of it. Importantly, the image duplicates the motion of the object along the axis perpendicular to the mirror.
03

Calculate the Speed of the Image

Because the car is moving at a velocity of \(30 \mathrm{~m/s}\) towards the mirror, its image moves towards the mirror (or away from the mirror) at the same speed of \(30 \mathrm{~m/s}\) in the opposite direction.
04

Determine Relative Speed

The relative speed of two moving objects is the sum of their speeds towards each other. The car moves towards the mirror at \(30 \mathrm{~m/s}\) and the image moves towards the car at \(30 \mathrm{~m/s}\), so their relative speed is \(30 + 30 = 60 \mathrm{~m/s}\).

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Key Concepts

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

Plane Mirror
A plane mirror is a flat, reflective surface that forms images by bouncing light off its surface. This type of mirror is very common and is used in everyday objects like bathroom mirrors and dressing mirrors.
When we look into a plane mirror, we see a reflected image of ourselves. This image appears to be the same distance behind the mirror as we are in front of it.
  • The image is virtual, meaning it can't be projected onto a screen.
  • The image is upright and has the same size as the object.
  • Plane mirrors exhibit lateral inversion, flipping the image left to right.
This principal understanding of how plane mirrors work is critical in grasping concepts related to image movement and speed calculation.
Image Formation
Image formation in a plane mirror occurs due to the reflection of light. The light rays bouncing off an object reflect off the mirror to form an image that our eyes perceive.
Here鈥檚 how it works:
  • The object emits or reflects rays of light.
  • These light rays strike the plane mirror at various angles.
  • According to the law of reflection, the angle of incidence equals the angle of reflection.
  • The light rays diverge, creating an image that appears to be behind the mirror.
Because the brain interprets these light rays as coming from a straight line path, we see a mirrored image. Understanding this process helps explain why the image moves along with the object but in the opposite direction.
Velocity Calculation
Calculating the velocity of images in a plane mirror involves understanding relative velocity. In our scenario, the car is approaching the mirror.
The image creates a mirrored movement that matches the car鈥檚 speed but in the opposite direction.
  • If a car moves towards the mirror at a speed of 30 m/s, the image moves towards the car at 30 m/s in reverse direction.
  • To find the relative speed of the image with respect to the car, you add the speeds (30 m/s of the car + 30 m/s of the image).
  • This results in a relative speed of 60 m/s.
This example of relative speed shows how movements appear when viewed in relation to another moving object, providing insight into both physics and daily experiences with motion and reflection.

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Most popular questions from this chapter

A point source \(S\) is centred infront of a \(70 \mathrm{~cm}\) wide plane mirror. A man starts walking from the source along a line parallel to the mirror. The maximum distance that can be walked by man without losing sight of the image of source is: (a) \(80 \mathrm{~cm}\) (b) \(60 \mathrm{~cm}\) (c) \(70 \mathrm{~cm}\) (d) \(90 \mathrm{~cm}\)

A plane mirror which rotates \(10^{4}\) times per minute reflects light on to a stationary mirror \(50 \mathrm{~m}\) away. This mirror reflects the light normally so that it strikes the rotating mirror again. The image observed in the rotating mirror is shifted through \(2.4\) minutes from the position it occupies. When the rotating mirror is stationary, what is the speed of light? (a) \(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\) (b) \(4 \times 10^{8} \mathrm{~m} / \mathrm{s}\) (c) \(5 \times 10^{8} \mathrm{~m} / \mathrm{s}\) (d) \(6 \times 10^{8} \mathrm{~m} / \mathrm{s}\)

The shortest height of a vertical mirror required to see the entire image of a man, will be (a) one-third the man's height (b) half the man's height (c) two-third the man's height (d) data insufficient

A rear view mirror of a vehicle is cylindrical having radius of curvature \(5 \mathrm{~cm}\) and length of arc of curved surface is \(10 \mathrm{~cm}\). The field of view in radian, if it is assumed that the eye of the driver is at a large distance from the mirror, is: (a) \(0.5\) (b) 1 (c) 2 (d) 4

A plane mirror is placed in \(y-z\) plane facing towards negative \(x\) -axis. The mirror is moving parallel to \(y\) -axis with a speed of \(5 \mathrm{~cm} / \mathrm{s}\). A point object \(P\) is moving infront of the mirror with a velocity \(3 \hat{i}+4 \hat{j}\). The velocity of image is: (a) \(-3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}\) (b) \(3 \hat{i}-4 \hat{j}\) (c) \(-3 \hat{i}\) (d) \(3 \hat{i}+4 \hat{j}\)
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