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Chapter 19: Problem 52

If an object is placed between two plane mirrors. a distance \(2 b\) apart, the object is situated at mid-point between mirrors, the position of \(n^{\text {th }}\) image formed by one of the mirrors with respect to the object is: (a) \(n b\) (b) \(2 n b\) (c) \(3 n b\) (d) \(4 n b\)

Short Answer

Expert verified
Option (b) 2nb

Step by step solution

01

Understanding the Problem

We have two plane mirrors placed opposite to each other at a distance of \(2b\). An object is placed midway between them. We need to find the position of the \(n^{th}\) image formed by one of the mirrors relative to the object.
02

Recognizing Image Formations

Plane mirrors create images by reflecting light. When an object is placed between two mirrors, multiple images form due to repeated reflections. The first image forms behind the mirror at the same distance as the object is in front of it.
03

Identifying Image Pattern

In this setup, each mirror creates images of both the object and the images formed by the opposite mirror. The mirrors reflect images alternately, and each subsequent reflection occurs at an additional distance equal to the separation between the mirrors, which is \(2b\), in this case.
04

Finding the nth Image Position

For the \(n^{th}\) image observed in one of the mirrors, each successive image is positioned \(2b\) further from the previous image. Hence, the distance covered for the \(n^{th}\) image is \(2nb\).
05

Selecting the Correct Answer

Given the pattern of image formation, the position of the \(n^{th}\) image relative to the object will be \(2nb\). Thus, the correct answer is option (b) \(2nb\).

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Key Concepts

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

Image Formation
When we talk about image formation, especially with plane mirrors, we're really talking about how light behaves when it encounters reflective surfaces. A plane mirror creates an image that appears to be behind the mirror. This happens because light rays bounce off the mirror and into our eyes, making it seem as if the image is located somewhere it鈥檚 not.

Here's the interesting part about plane mirrors:
  • The image is always upright, meaning it looks like the object, but reversed from left to right, just like looking in a mirror.
  • Images produced by plane mirrors are virtual. This means they cannot be projected onto a screen.
  • As a rule of thumb, the distance from the object to the mirror is the same as the distance from the image to the mirror.
This consistent behavior helps in predicting the formation of images especially when there are multiple mirrors involved.
Reflection of Light
Reflection of light is a key concept in understanding how plane mirrors work. When light strikes a surface, it bounces back. This bouncing back is called reflection. Plane mirrors, being flat and smooth, reflect most of the light uniformly. To describe this reflection, we use a simple rule called the law of reflection.

The law of reflection states:
  • The angle of incidence (the angle at which the incoming light hits the surface) is equal to the angle of reflection (the angle at which it leaves the surface).
  • This principle allows mirrors to create clear and precise images, as all incoming light waves are bounced back at consistent angles.
In the setup with two opposite mirrors, light reflects back and forth, creating multiple images in the process. Understanding reflection helps explain why images appear to float between the mirrors.
Distance Between Mirrors
The concept of the distance between mirrors comes into play in scenarios involving multiple reflections, such as when two mirrors face each other. In the given problem, the two mirrors are placed a distance of \(2b\) apart with an object perfectly centered between them.

This specific arrangement leads to fascinating patterns of image formation. As each mirror reflects both the original object and the images created by the opposite mirror, this results in a series of images appearing to cascade between the mirrors.
  • With every reflection, additional distance equal to the separation (\(2b\) in this case) gets added to the position of the succeeding image.
  • So, for the \(n^{th}\) image in a single mirror, the total distance from the original object is \(2nb\).
  • Understanding this repeating pattern is essential to predict where multiple images will form.
This predictable increment in distance is due to consequent reflections, making calculations both simple and logical once recognized.

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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 point object \(P\) is placed at centre of curvature of a concave mirror of focal length \(25 \mathrm{~cm}\). The mirror is cut into two halves and shifted symmetrically \(1 \mathrm{~cm}\) apart in perpendicular to the optical axis. The distance between images formed by both parts is: (a) \(2 \mathrm{~cm}\) (b) \(1 \mathrm{~cm}\) (c) \(3 \mathrm{~cm}\) (d) \(4 \mathrm{~cm}\)

If \(u\) represents object distance from pole of spherical mirror and \(v\) represents image distance from pole of mirror and \(f\) is the focal length of the mirror, then a straight line \(u=v\) will cut \(u\) versus \(v\) graph at : (a) \((f, f)\) (b) \((2 f, 2 f)\) (c) \((f, 2 f)\) (d) \((0,0)\)

A body of mass \(100 \mathrm{~g}\) is tied to one end of spring of constant \(20 \mathrm{~N} / \mathrm{m}\). The distance between pole of mirror and mean position of the body is \(20 \mathrm{~cm}\). The focal length of convex mirror is \(10 \mathrm{~cm}\). The amplitude of vibration of image is :(a) \(10 \mathrm{~cm}\) (b) \(50 \mathrm{~cm}\) (c) \(0.67 \mathrm{~cm}\) (d) \(0.33 \mathrm{~cm}\)

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) \(4 \mathrm{~m}\)
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