Chapter%201 reflecting%20light

8/14/2019 Chapter%201 reflecting%20light

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Chapter 1_Reflecting Light

Main Ideas

1. Light and its properties2. Plane mirror reflection3. Regular and diffuse reflection4. Forming images with a plane mirror5. Concave mirrors6. Convex mirrors7. Using concave mirrors in the reflecting telescope8. Problems with curved mirrors

Theory Various Background

INTRODUCTION

Light is fascinating. It brings the energy from the Sun needed to power the living world and sustain our life. Our eyes use

it to form images of the world around us. It always moves at the fastest speed possible in the universe, 300 million meters/sec.

Furthermore, the speed of light doesnt depend on the motion of the source which emitted it or the motion of the observer which

detects it. No matter particles can move as fast as light irrespective of how much energy is used to accelerate them.

And that is only part of the story. Light is neither a wave nor a stream of particles although it has particle-like properties

and wave-like properties. (Light is not alone in this regard; all matter also exhibits both wave-like and particle-like properties).

Our understanding of the nature of light has gone through several revolutions since the time of Newton. Although we

understand much more about light than ever before, a deep understanding of its nature still eludes us. Einstein contributed

greatly to our understanding of light. Before he died he said,

And these fifty years of conscious brooding have brought me no nearer to the question of What are light

quanta? Nowadays every clod thinks he knows it, but he is mistaken.

BASIC LIGHT PROPERTIES

Light can be thought of as a form of energy which moves according to 3 basic properties:

It travels in straight lines It requires no medium for transmission It travels at a speed of 3 108 m/s in a vacuumThe sun is the source of most of the light we see. Without light we find it impossible to see anything.LUMINOUS AND NON-LUMINOUSObjects that emit their own light are called luminous. Luminous objects include a candle flame, a star, a glowing electric light bulb

and burning magnesium.

We see most other objects because they reflect light. These are called non-luminous. This page, your desk, the moon and you are

non-luminous.

RAYS AND BEAMSUsually light travels in straight lines, whether it is emitted or reflected, until it meets something that changes its direction. The path

of light can be represented by light rays which we draw as straight lines. A set of light rays is called a light beam. A set of rays can

be described as either parallel to each other, divergent or convergent.

SHADOWSAs light travels in straight lines, a point source of light placed in front of an opaque body will produce on a screen a clean edged

shadow.


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When a source of some magnitude is placed in front of an opaque object its total shadow can be seen as two parts, an area of

complete shadow (Umbra), surrounded by an area of partial shadow (Penumbra).

This can readily be seen using an ordinary light bulb. A total eclipse (umbra) and a partial eclipse (penumbra) occur on Earth when

the moon passes in front of the sun (a source of some magnitude).

SPEED OF LIGHT

Light travels extremely fast. The current estimate for the speed of light in vacuo is 299 793 km/s. Approximated at 3 108 m/s. At

this speed, light travels around the earth 7 times each second.

REFLECTIONWe see most objects around us because they reflect light. A plane sheet of paper does not reflect light the same way as a plane

mirror. Light reflecting from this page is scattered and the reflection is called diffuse. The light is scattered on reflection because

this page is not smooth. We can see this page but we cannot see other things reflected in the page. Mirrors are smooth reflectors, so

light is reflected in an ordered manner, so we see images. This type of reflection is called specular.

Light Rays

Because rays of light travel in straight lines, we can draw them as lines in diagrams

Reflection of Light

Light hitting the mirror is called the incident ray. Light leaving the mirror is called thereflected ray.

i r

incident ray reflected ray

normal

Most objects we see reflect light rather than emit their own light.Law of Reflection

The angle of incidence equals the angle of reflection. This is true for both flat mirrors and curved mirrors.

Types of Reflection

Specular Reflection - images seen on smooth surfaces (e.g. plane mirrors) Diffuse Reflection - diffuse light coming from a rough surface (cannot see a reflection of yourself)


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How do we make light? Heat and Light: Incandescent Lighting (3-5% efficient) Atoms and Light: Fluorescent Lighting (20-40% efficient)

Heat and Light

The way we see most things is by shining light on them, and then looking at the light reflected from the object. The way we see stars is not this way. We see the light that comes solely from the object itselfrather than light reflected

from some other source. This type of radiation is called blackbody radiation since there is no reflected light involved,

and things that dont reflect light normally look black.

Atoms and Light

When we excite atoms with energy, we find that the atoms emit light. However, they do not emit light in a continuous spectrum (all

colors) like hot objects do. Rather, they emit only certain colors of light, which we call a discrete spectrum, or an emission

spectrum. Each element emits its own individual spectrum. Several examples will be demonstrated in class.

Hydrogens spectrum (in the visible) consists of just three lines: purple, blue-green, and red.

Helium has quite a bit different set of lines in its spectrum.

Electromagnetic Wave Velocity

The speed of light is the same for all seven forms of light. It is 300,000 kilometers per second or 186,000 miles per second.


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The Electromagnetic Spectrum

Radio Waves - communication Microwaves - used to cook Infrared - heat waves Visible Light - detected by your eyes Ultraviolet - causes sunburns X-rays - penetrates tissue Gamma Rays - most energetic

The Visible Spectrum

A range of light waves extending in wavelength from about 400 to 700 namometers.


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Transparent Materials

Transparent - the term applied to materials through which light can pass in straight linesOpaque Materials

Opaque - the term applied to materials that absorb light Are clouds transparent or opaque to visible light?

Answer: opaque

Are clouds transparent or opaque to ultraviolet light? Answer: transparent

Shadows

Shadows are formed when an object blocks out the light.


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Lampobject

screen

umbra

penumbra

Umbra - the darker part of a shadow where all the light is blocked Penumbra - a partial shadow These terms also apply to Solar Eclipses and Lunar Eclipses.

A solar eclipse occurs when the Moon passes in front of the Sun.

A lunar eclipse occurs when the Moon passes into the Earth's shadow.


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Plane Mirrors

The law of reflectionConsider the figure below. The red line is the normal, which is an imaginary line that is perpendicular to the mirrors surface at the

point where the incident (incoming) ray is striking the mirror.

The law of reflection states that the angle of incidence, i, is equal to the angle of reflection, r. Therefore i = r

Your eyes focus the diverging rays from your friends foot in order for you to see them.


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When diverging rays from you own foot are reflected back at you your eyes focus them and you interpret the information as there

being another body behind the mirror.

Your virtual image will be the same distance behind the mirror as you are in front of the mirror.

IMAGES IN PLANE MIRRORSThe image of an object in a plane mirror is:-

1. upright2. the same size as the object3. as far behind the mirror as the object is in front4. on the perpendicular from the object to the mirror5. laterally inverted the right side of the object, when viewed directly, appears to be the left hand side of the object when

viewed using a mirror.

6. Virtual, as the rays only appear to come from the image.MULTIPLE MIRRORSIf 2 plane mirrors are arranged at right angles to each other, incident light will reflect from one mirror and then the other. The

reflected ray will emerge parallel to the incoming ray. If the angle between the mirrors is reduced the number of images is given by

1

3600

PERISCOPESA periscope consists of two plane mirrors arranged at opposite ends of a tube. One end of the tube is open for viewing and the other

faces the scene you wish to view.

Each mirror is arranged across the tube at an angle of 45 to the side of the tube. Light enters the top of the tube, hits the top mirror

and is reflected down the tube to the bottom mirror. When the light hits the bottom mirror it is reflected into your eyes. The image

that you see is exactly the same as the object, unlike the lateral inversion that you experience with a single plane mirror.

Periscopes are used to see over the top of obstacles. In submarines under the sea, periscopes are used to observe the sea surface.

They are also used in a double decker bus to enable the driver to see people in the upper deck.

OPAQUE MATERIALSThings we see appear to be different colours because of the way in which they absorb, transmit or reflect different parts of the

visible spectrum.Opaque materials do not transmit any light. They appear coloured because of the light they reflect. Blue surfaces reflect blue light,

and absorb the others. Black surfaces absorb all the different colours and white surfaces reflect all the different colours. Paints are

examples of opaque material.

TRANSPARENT MATERIALSTransparent materials allow light to pass through them. They also absorb all the colours of the visible spectrum except those that

give them their colour. Unlike opaque material, transparent materials transmit as well as reflect the parts of the visible spectrum

that give them their colour. A piece of red cellophane transmits and partially reflects red light, but absorbs other colours.

VIRTUAL AND REAL IMAGESA real image is where the rays converge to meet in reality, ie. Can be shown on a screen. A virtual image is where the rays appear

to converge, eg. A plane mirror. With a virtual image your brain interprets the information it is receiving by imagining an image

there.


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Curved Mirrors

The inside of a soupspoon, the mirrors used in flash bulbs, car headlights are all examples of mirrors that curve inwards.

Spherical Mirrors

Spherical mirrors are of two types, concave (converging) and convex (diverging). The centre of the sphere of which the mirror

forms part of is called the centre of curvature (C). The central point of the mirror is called the pole (P). The line passing through

the pole and the centre of curvature is called the principal axis. The aperture (A) is the diameter of the circular face of the mirror.

The radius of curvature (r) is the distance between the pole and the centre of curvature. The focal point or principal focus (F) is

the point, through which the rays of light parallel to the principal axis either pass or appear to pass. The focal length (f) is the

distance between the pole and the focal point. The radius of curvature is always twice the focal length. That is: r = 2f

Parallel Rays

Rays of light striking an object, from a source an infinite distance away will be parallel to each other.

If the rays of light are parallel to each other, but not parallel to the principal axis, the image will not be at the principal focus, but

will be in the focal plane. That is the plane perpendicular to the principal axis and passing through the principal focus.

The line from the centre of curvature to a point on the mirror is perpendicular to the mirror at that point. Thus it is the normal at thatpoint. So, if necessary, to complete the diagram, use the second law of reflection of light.


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Describing images

Images are described by

Nature is the image real or virtual Orientation is the image upright or inverted Position where is it in relation to the pole of the mirror Size (what is the height of the image) and magnification.Locating imagesWe use a technique called ray tracing to predict where a curved mirror will form an image, and to find the size and type of that

image. Ray tracing requires us to draw a diagram, showing the curved mirror in cross-section.To locate the position of the image of an object of some size, two rays are required. Either

(i) a ray parallel to the principal axis, which passes through the focus or appears to come from the focus,

(ii) a ray passing through the centre of curvature, which is reflected back through the centre of curvature,

(iii) a ray incident at the pole, which is reflected so that the incident ray and the reflected ray make the same angle with theprincipal axis.


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(iv) a ray passing through the principal focus, which is reflected parallel to the principal axis,

In order to locate an image only two rays from the object are needed. Remember though that the object actually emits rays in all

directions.

We can see, from the construction of the images, that when the object gets nearer to the principal focus, the size of the image is

larger. This is true for both real and virtual images. The size of the image becomes infinitely large when the object is at the

principal focus. We also see that the real images are always inverted and virtual images are always upright.

If the object is not on the principal axis the image will not be on the principal axis.

Magnification

The magnification of an image is given by the ratio M =heightObject

heightImage=

distanceObject

distanceImage

Mu

v

H

H

o

i==


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Summary Concave mirrors

Position of object Position of image Description of image

Beyond C Between C and F Real Inverted Diminished

At C at C Real Inverted Same size

Between C and F Beyond C Real Inverted Enlarged

At F No image - - -

Beyond F Behind mirror Virtual Upright Enlarged

Convex mirrors

Mirrors that have their reflective surfaces on the outside of a curve are called convex mirrors. Just as with a concave mirror, we

can model a convex mirror with many small plane mirrors. A parallel sat of rays travelling towards the plane mirrors will spread

out after reflection. The rays appear to come from a point behind the mirror, this is called the virtual focal point of the mirror. Asthe rays diverge from a convex mirror it can be called a diverging mirror.

The main advantage of the convex mirror is that it gives a wide field of view, ie. an image can be formed of large objects.

The mirror formula

The mirror formula is a relationship between the focal length of a mirror, f, the distance the object is from the pole of the mirror, u,

and the distance of the image from the pole of the mirror, v. See page 28 for the derivation of this formula.

There are several useful formulae that can be used to solve mirror problems. I see them as a last resort, a good ray diagram is much

more powerful.


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The relationship is:

vuf

111+=

where f is the focal length

u is the object distancev is the image distance

The sign conventions for u, v and f, are: f is positive for a concave mirror and negative for a convex mirror. v is positive for a realimage and negative for a virtual image. u is always positive since objects are always placed in front of mirrors.

MagnificationThe magnification of an image is given by the ratio:

m =objecttheofHeight

imagetheofHeight=

distanceObject

distanceImage

The abbreviations are as follows mu

v

H

H

o

i==

The minus sign indicates that the image is inverted.

If M > 1 the image is magnified. IfM < 1 the image is diminished.


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Ray tracingRAY 1

This ray travels parallel to the principal axis and reflects as if it came from the virtual focus of the mirror.

RAY 2

This ray travels towards the centre of curvature of the mirror and strikes the mirror surface along the normal at the point, i.e. the

angle on incidence is 0 degrees, and so it will reflect along the path it came from whence it came.

RAY 3

The ray strikes the pole of the mirror and reflects at an angle equal to the angle of incidence. The principal axis acts as the normal at

this point, and you can treat this point of the mirror as a plan mirror.

RAY 4

The ray of light directed at the virtual focal point reflects parallel to the principal axis.


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Finding the image

When constructing a ray diagram for a convex mirror, the same conventions apply as for concave mirrors.

Summary of Convex mirrors

Rays parallel to the principal axis will diverge on reflection from a convex mirror. They reflect as they appearto come fromthe focal point on the other side of the mirror.

A ray aimed at the virtual focal point on the opposite side of the mirror will be reflected by the mirror so that it emerges parallelto the principal axis.

A convex mirror is useful because it has a wide field of view and always produces upright images. The focal length of a spherical mirror is half its radius of curvature. Convex mirrors always produce virtual, upright, diminished images.

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Chapter%201 reflecting%20light