Reflection Refraction Study Sheet

8/3/2019 Reflection Refraction Study Sheet

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Reflection and Refractionand Mirrors and Lenses

RaysUsually light travels in straight lines, whether it is emitted or reflected, until it meets somethingthat changes its direction. In this case, we view the light wave as a ray, which is always normal to

the surface of the wave front. The path of light can be represented by light rays, which we drawas straight lines. A set of light rays is called a light beam.

Reflection and RefractionWaves can be reflected and refracted by various surfaces placed in the path of the wave.Consider a light ray that is incident on a plane glass surface.

n2

1

n3

n11

2

3

We see that the beam is partially reflected and partially transmitted. The transmitted beam is bentboth upon entering the surface and upon exiting it. Let 1 be the angle the incident beam makeswith the normal to the surface of the glass. Also, let 1 be the angle the reflected beam makeswith the normal, let 2 be the angle of the beam in the glass surface, and let 3 be the angle ofthe beam that exits the glass surface. The reflected and refracted rays lie in the plane formed bythe incident ray and the normal to the surface at the point of incidence. This plane is called theplane of incidence. The incident and reflected rays are equal, that is, 1' = 1. This is called thelaw of reflection.

MirrorsConsider a plane mirror.

P

P


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The figure shows a narrow bundle of light rays coming from a point source P reflected in a planemirror. After reflection, the rays diverge exactly as if they came from a point P' behind the plane ofthe mirror. The point P' is called the image of the object P. When these rays enter the eye, theycannot be distinguished from rays diverging from a source P' with no mirror. The image is called avirtual image because the light does not actually emanate from the image but only appears to.Geometric construction using the law of reflection shows that the image lies on the line throughthe object perpendicular to the plane of the mirror and at a distance behind the plane equal to thedistance from the plane to the object. If the source is an extended object:

A mirror image is upright, but appears reversed right to left.

A mirror image appears to be the same distance behind the mirror that the object is infront of the mirror.

A mirror image is the same size as the object.

Spherical MirrorSpherical mirrors are of two types, concave (converging) and convex (diverging).

The center of the sphere of which the mirror forms part of is called the center of curvature (C).The central point of the mirror is called the pole (P). The line passing through the pole and thecenter of curvature is called the principal axis. The radius of curvature (r) is the distancebetween the pole and the center of curvature. The focal point orprincipal focus (F) is the point

through which the rays of light parallel to the principal axis either pass or appear to pass. Thefocal length (f) is the distance between the pole and the focal point. The radius of curvature isalways twice the focal length. That is r = 2f

C

FP

P

P'


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The figure above shows a bundle of rays from a point on the axis of a concave spherical mirrorreflecting from the mirror and converging at point P'. The rays then diverge from this point just asif there were an object at that point. This image is called a real image because the light actuallydoes emanate from the image point. It can be seen by an eye placed to the left of the imagelooking into the mirror. It could also be observed on a viewing screen placed at the image point. Avirtual image cannot be observed on a screen at the image point because there is no light there.Despite this distinction between real and virtual images, the light rays diverging from a real imageand those appearing to diverge from a virtual image are identical, so that no distinction is madeby the eye when viewing either a real or virtual image.

Mirrors that have their reflective surfaces on the outside of a curve are called convex mirrors. Aparallel sat of rays travelling towards a convex mirror will spread out after reflection. The raysappear to come from a point behind the mirrorthis is called the virtual focal point of the mirror.Convex mirrors always produce virtual, upright, diminished images.

Law of RefractionA ray of light travels along a straight path within the same medium (eg. air, water, or glass).However, experiments show that when a ray of light enters one medium from another, the rayoften changes direction at the point of incidence. This change of path is due to refraction.Refraction is the bending of the light path as it passes from one transparent material to another.

The angle between the incident ray and the normal to the boundary between the two media iscalled the angle of incidence. The angle between the refracted ray and the normal is called theangle of refraction. The change of direction depends on the angle of incidence and the media.This bent or refracted ray relates with the incident ray by the so-called laws of refraction:

The refracted ray is in the same plane as the incident ray and the normal to the mirror atthe point of incidence, but on the opposite side of the normal from the incident ray.

For two particular media, the ratio of the sine of the angle of incidence to the sine of theangle of refraction is constant, i.e.

constantsin

sin

2

1=

i

i

This constant depends on the nature of the media. It is called the relative refractive index. Thisequation is known as Snells Law. The relative refractive index is often labelled as 1n2, hence wehave:

21

2

1

sin

sinn

i

i=

The absolute refractive index of a substance is the relative refractive index from a vacuum (n =1.00) to the substance. The refractive index of air is so close to 1.00 that for practical purposes,its value is taken to be exactly 1.00. The refractive index for glass varies with the composition ofthe glass. The most common value is 1.5. An important relation for the refractive indices of twomedia:

1

2

2

1

sin

sin

n

n

i

i=

,

or

,2211sinsin inin =


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Where n1 and n2 are absolute refractive indices of the two media.

The relative refractive index of the two media is the ratio of the speeds of light in the two media.For a ray of light travelling from medium A to medium B:

1 2

2 1

sin

sin

i n v

i n v= =

1

2

Where v1 is the speed of light in medium A and v2 is the speed of light in medium B. Also, theexpression:

1 1 1 1

2 2 2 2

sin sin

sin sin

i i v f gives

i i v f

1

2

= = = .

In going from a medium with a small absolute index of refraction to one with a large absoluteindex of refraction, the ray will bend toward the normal. In going from a medium with a large indexof refraction to one with a small index of refraction, the ray will bend away from the normal. Wesay that a material is optically denser if it has a higher absolute refractive index. Light is refracted

toward the normal when it travels into a medium of higher optical density. Optical density anddensity are not related.

Total Internal ReflectionRecall that when light goes from a more optically dense medium to a less dense medium (e.g.from glass to air) the refracted ray is bent away from the normal. The refracted angle increaseswith the incident angle. When the refracted angle equals 90, the incident angle is said to be thecritical angle. We can find the critical angle, c , from Snell's Law. Let n2 < n1. Then if we set1= c and = 90 we get:2

( )21 1 21 1

sin 90sin sinc

n n

n n

= =

Further increase in the incident angle will cause total internal reflection, all the incident light isreflected back into the incident medium, and no refracted ray exists. No refraction occursbecause in this case Snells Law would imply a refracted angle having sin 1 > 1, which ismathematically impossible. Fibre optics confine light beams in a bent glass rod.

LensesA lens is made of any transparent material bounded by curved surfaces. Each of a lens's twofaces is part of a sphere with a refractive index greater than that of the air. One face may also beplane or flat. A lens is called a convex lens if it is thicker at the center than at the edges, and it iscalled a concave lens if it is thinner at the center than at the edges. Lenses cause a beam of lightto bend on passing through it. Converging lenses are convex and diverging lenses are concave.

Converging lenses bend the light in such a way that as light rays pass through, they cometogether. Diverging lenses bend light so that the rays spread out.

The line joining the center of curvature of the two surfaces is the principal axis of the lens. A lenshas two symmetrically located focal points on its central axis, one on either side, with theproperties that:

An incident ray parallel to the central axis is refracted through the focal point.

An incident ray through the focal point is refracted parallel to the central axis.


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By drawing rays of these two types, one can construct a ray diagram to determine the locationand orientation of the image formed by an object.

Images Formed by LensesTo locate the position of the image of an object, two of the following rays are required:

A ray leaving the same point on the object, through the center of the lens, which isundeviated.

A ray parallel to the principal axis, which passes or appears to pass through the principalfocus.

A ray passing or appearing to pass through the principal focus, emerging from the lensparallel to the principal axis.

Images are described by:

Nature:is the image real or virtual Orientation:is the image upright or inverted

Position:the distance of the image from the optical axis

Size:what is the height of the image Magnification:The magnification produced by a lens is defined by m, where

height of imagem

heightof object= .

Ray tracing:

Locate object

Draw ray from the top of the arrow through center of lens and extend on the rear side.

Draw a parallel ray to the principal axis. This ray refracts from the principal plane andpasses through rear focal point.

Extend this last ray back to the front side of the lens.

The image is formed where rays meet.

Examples

Convex Lens.Object beyond "f".

principal axis

f

imageobject

principal plane

f

front rear

The image is real and inverted; image will be smaller than object


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Convex Lens.

Object between end and "f":

principal axis

f

image

object

principal plane

f

front rear

The image is virtual and erect; image will be larger than object

Concave Lens

The image is virtual, upright and diminished.

principal axis

f

image

object

principal plane

f

frontrear

Thin-lens EquationIf s0 and s1 denote the distances of an object and image from the lenss center, respectively, and fdenotes the lenss focal length, then:

fss

111

io

=+

A negativevalue of s1 indicates a virtual image (on the same side of the lens as theobject), which will be produced by a converging (convex) lens whenever the object iscloser to the lens than the focal length.


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A negativevalue offdenotes a diverging(concave) lens (which alwaysproduces virtualimages).

The magnification produced by a lens is defined by m, where:

1

0

sheight of imagem

heightof object s= =

1

0

sheight of imagem

height of object s= = .or

Sign ConventionThe complete sign convention for mirrors and lenses:

R radius of curvature + for converging, - for diverging

f focal length + for converging, - for diverging

s object distance + for real objectos image distance + for real images, - for virtual imagesih object size + if upright, - if invertedo

image size + if upright, - if invertedhi

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