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Chapter 19: Problem 32

A plane mirror is mounted parallel to a vertical wall at the distance ' \(d^{\prime}\) from light fixed on the wall gets reflected by the mirror to form a path of light on the wall. When the mirror is moved parallel to itself towards the wall, the path of light on the wall: (a) remains unchanged in position and vertical height (b) moves along the wall away from the source without changing in vertical length (c) will increase in vertical length with the lower end fixed (d) moves along the wall away from the source and is increasing in vertical length.

Short Answer

Expert verified
(d) The path moves away and increases in length.

Step by step solution

01

Understanding the Setup

The problem involves a plane mirror reflecting a path of light from a fixed source on the opposite wall back onto the same wall. We need to understand how shifting the mirror affects the light path on the wall.
02

Conceptual Analysis of Mirror Movement

When the mirror moves closer to the wall, the path of the reflected light changes. Since the light path is from the wall to the mirror and back, reducing the distance between the mirror and the wall changes the angle at which light hits the wall.
03

Result of Moving the Mirror

As the mirror moves closer, the angle of incidence on the mirror changes, resulting in the light path on the wall moving away from the source and elongating vertically.
04

Verification through Reflection Principles

According to the laws of reflection, the angle of incidence equals the angle of reflection. As the angle changes with the movement of the mirror, the elongation and movement of the reflected light path can be deduced.

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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, smooth reflective surface that bounces light in a defined way. When light hits the surface of a plane mirror, it doesn't scatter in different directions.
Instead, it reflects in a predictable manner based on its angle of approach. The property that defines this predictable behavior derives from the laws of reflection that we'll explore in this article.

Plane mirrors are commonly used because they maintain the integrity of the light path's form, hence rendering images and reflections that are uniform and accurate.
  • They don't distort the size of the image but can change its orientation.
  • The images seen in plane mirrors are always virtual, upright, and the same size as the object.
Plane mirrors are integral components in various applications鈥攆rom household mirrors to complex scientific instruments.
Angle of Incidence
The concept of "Angle of Incidence" is fundamental in understanding how light interacts with surfaces. In simple terms, when a light ray reaches a surface, the angle between this incoming light ray and the normal (a line perpendicular to the surface at the point of contact) is known as the angle of incidence.
It's crucial because it determines how the light behaves upon reflection.

According to the laws of reflection, the angle of incidence is equal to the angle of reflection. This law holds true for all types of mirrors but is easiest to observe in plane mirrors due to their flat surface.
  • If the angle of incidence is 30 degrees with respect to the normal, the angle of reflection will also be 30 degrees.
  • This angle influences the direction in which light is reflected from the mirror, affecting where it will land or how it will extend.
In the original problem, changes in the angle of incidence are why moving the mirror alters the path and length of the reflected light on the wall.
Angle of Reflection
The angle of reflection is as essential as the angle of incidence in understanding reflection through surfaces. It is the angle formed between the reflected ray and the normal to the surface at the point of incidence.
According to the law of reflection, the angle of reflection is equal to the angle of incidence, which is a core principle that governs the behavior of light when it encounters surfaces.

This concept ensures that the path of light is symmetrical with respect to the normal. In the context of our original exercise, when the plane mirror is moved closer to the wall:
  • The angle of incidence changes, consequently changing the angle of reflection.
  • The result is a light path on the wall that moves and extends away from the source.
Understanding how the angle of reflection works helps in predicting and explaining the behavior of light paths in various setups.

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Most popular questions from this chapter

A flat mirror revolves at a constant angular velocity making 2 revolutions/sec. With what velocity will a light spot move along a spherical screen with a radius of \(10 \mathrm{~m}\), if the mirror is at a centre of curvature of the screen? (a) \(251.2 \mathrm{~m} / \mathrm{s}\) (b) \(261.2 \mathrm{~m} / \mathrm{s}\) (c) \(271.2 \mathrm{~m} / \mathrm{s}\) (d) \(241.2 \mathrm{~m} / \mathrm{s}\)

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 bullet of mass \(m_{2}\) is fired from a gun of mass \(m_{1}\) with horizontal velocity \(v .\) A plane mirror is fixed at gun facing towards bullet. The velocity of the image of bullet formed by the plane mirror with respect to bullet is: (a) \(\left(1+\frac{m_{2}}{m_{1}}\right)\) (b) \(\left(\frac{m_{1}+m_{2}}{m_{1}}\right) v\) (c) \(\frac{2\left(m_{1}+m_{2}\right)}{m_{1}} v\) (d) none of these

A pole \(5 \mathrm{~m}\) high is situated on a horizontal surface. Sun rays are incident at an angle \(30^{\circ}\) with the vertical. The size of shadow on horizontal surface is : (a) \(5 \mathrm{~m}\) (b) \(\frac{5}{\sqrt{3}}=\mathrm{m}\) (c) \(\frac{10}{\sqrt{3}} \mathrm{~m}\) (d) none of these

Infront of a vertical wall, a plane mirror of square shape is mounted parallel to the wall at some distance from it. On the wall, a point light source is fixed and light from it gets reflected from the mirror and forms a path on the wall. If the mirror is moved parallel to itself towards the wall, then (i) centre of the patch may remain stationary (ii) the patch may remain square in shape (iii) area of patch decreases Choose correct statement: (a) (i) and (ii) are correct (b) (i) and (iii) are correct (c) (ii) and (iii) are correct (d) none of the above
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