Light Geometric Optics Key Concepts

8/3/2019 Light Geometric Optics Key Concepts

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LIGHT AND GEOMETERIC OPTICS

ATWOODS MACHINE

1. ELECTROMAGNETIC WAVES

White light is a mixture of all visible colors. When a beam of white light passesthrough a glass prism, the resulting beam is dispersed into a spectrum of colors.Dispersion of light in a transparent material occurs because the index of refraction of thematerial varies with wavelength, with higher indices corresponding to shorter wavelengths.

Wavelengths in the narrow, visible light spectrum range from 750 nm for the colorred down to 400 nm for the color violet as shown below.

700 nm 400 nmWavelength,

Frequency, f4x1014 Hz 7.5x1014 Hz However, visible light makes up just a tiny portion of the large electromagnetic spectrum.Types of waves with longer wavelengths than visible light include infrared radiation,microwaves, and radio waves. Those with shorter wavelengths include ultravioletradiation, x-rays, and gamma-rays.

ELECTROMAGNETIC WAVES

(m) f(Hz)

radio waves 0.34 - 570 5x105

- 9x108

Hzmicrowaves 1x10-3 - 0.1 3x109 - 3x1011 Hz

infrared radiation (IR) 7x10-7

- 1x10-3

3x1011

- 4x1014

Hz

visible light (VIS) 4x10-7 - 7x10-7 4x1014 - 7.5x1014 Hz

ultraviolet (UV) 1x10-8 - 4x10-7 7.5x1014 - 3x1016 Hz

x-rays 1x10-11 - 1x10-8 4x1016 - 3x1019 Hz

gamma-rays < 1x10-11 > 3x1019 Hz

Because light is made up of transverse waves, it can be polarized. The direction of

polarization is taken to be the direction of the electric field vector. A special filter known asa polarizerproduces polarized light from unpolarized light. The same filter can be used asan analyzerto determine whether or not light is polarized. When the axis of the analyzer isparallel to the plane of polarized light, the greatest amount of light is transmitted. When theanalyzer is perpendicular to the plane of polarized light, no light transmission occurs.

2. REFLECTION & REFRACTION


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KEY CONCEPT LIGHT & GEOMETERIC OPTICS

Light is assumed to travel along straight-line paths known as rays. When lightstrikes a surface, some of it undergoes reflection. A light ray strikes a surface at a certain

angle of incidence, i relative to the surface normal, and is reflected at an identical angle

of reflection, r. This is the law of reflection as given by:

i

=

i r

If the surface of reflection is a flat, shiny mirror, the process is known as specularreflection. The law also holds fordiffuse reflection from a rough surface as long as eachsmall section of surface is considered separately.

If a light ray passes into a transparent medium at an angle 1 that is not equal to

90, the path of the ray bends. This bending of light is known as refraction, and the angle2 at which it is bent is known as the angle of refraction.

1

2

Light travels at a speed of c = 3.00 108 m/s in a vacuum, but travels slower inother transparent media such as water or glass. It is the wavelength of light, not the

frequency, that varies from medium to medium. The index of refraction n is the ratio ofthe speed of light in a vacuum cto the speed of light in another medium v as given by:

n =c

v

The index of refraction can never be less than one because v can never be greater than c.

When light passes from one medium to another medium, the angle of refraction 2depends on the angle of incidence 1 and the speed of light in the two media involved.Therefore, the index of refraction in first medium n1 is related to that in the second mediumn2by the equation:

n1sin

1= n

2sin

2

This relationship is known as Snells Law.

If light rays traveling in a medium with a high index of refraction strike a secondmedium with a lower index of refraction at an angle that is large enough, the rays cannot


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refract into the second medium, and all of the rays are reflected at the interface. Thisphenomenon is known as total internal reflection. The angle at which it occurs is givenby:

sinC =n2

n1

where the angle c is known as the critical angle.

2. MIRRORS & LENSES

When looking at a plane mirror, the image appears to be located behind the mirror.Because light rays do not actually pass through this image, it is known as a virtual image.In the case of a plane mirror, the image distancesi from the mirror is the same as theobject distanceso from the mirror.

The most common curved mirror is a spherical mirror. A concave orconvergingmirrorhas its reflecting surface on the inside of the sphere. Parallel light rays reflecting ona converging mirror converge to a focal pointFwhich is located midway between themirror and its center of curvatureC. Therefore, the focal lengthfof the mirror is half the

radius of curvature R. A convex or diverging mirror has its reflecting surface on theoutside of the sphere. Parallel light rays that are reflected by a diverging lens diverge as iftheir origin were a focal point behind the mirror.

FC F C

Converging Mirror Diverging Mirror

There are certain principle rays that are defined according to their path with respect to themirrors geometry. These include:

A parallel ray that is incident along a path parallel to the mirrors axis and isreflected through the focal point.

A chief ray that is incident through the center of curvature and is reflected backalong its incident path.

A focal ray that passes through the focal point and is reflected parallel to themirrors axis.

FC

Parallel ray

FC

Chief ray

FC

Focal ray


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The image formed by a converging mirror can be real or virtual, whereas the image formedby a diverging mirror can only be virtual. The image characteristics depend on the positionof the object relative to the mirror. For a converging mirror these characteristics can besummarized as follows:

Forso >R the image is real, inverted, and reduced.

Forso =R the image is real, inverted, and the same size.

ForR >so >f the image is real, inverted, and enlarged.

Forso =f the image is at infinity.

Forso


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F

Converging lens

F F

Diverging lens

F

A converging lens can form either a real or a virtual image, whereas a diverging lens iscapable of forming only a virtual image. The image characteristics depend on the positionof the object relative to the lens. For a converging lens these characteristics can besummarized as follows:

Forso > f the image is real and inverted, and it can be enlarged, reduced, or thesame size.

Forso

=f the image converges at infinity. Forso


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edges of openings or slits. The diffraction effect is greatest when the slit width is on theorder of the wavelength of light that is being diffracted.

In Youngs double-slit experiment, light emerging from the two slits is used as twocoherent sources. When the light is projected onto a screen, an interference patternappears that consists of a series of alternating bright and dark fringes around a centralmaximum. Because the bright fringes indicate constructive interference, the path

difference between two waves must be an integral number of wavelengths. The positionsof the bright fringes are given by the equation:

dsin= m m = 0,1,2,3,...

where dis the distance between slits, is the angle of the bright fringe from the center line,

is the wavelength of the illuminating light and m is the order number. Dark fringes occurwhen the path difference is an odd number of half wavelengths, and their positions aregiven by the equation:

dsin= m 2( ) m =1,3,5,...

For a single slit, the width of the central maximum of the diffraction pattern is twice

that of the side fringes. The positions of the dark side fringes are given by the equation:wsin= m m =1,2,3,...

where w is the slit width.

A diffraction grating is a device that consists of thousands of slits per centimeter.The conditions required for a diffraction grating to produce bright fringes are the same asfor the double-slit setup. Diffraction gratings produce very sharp bright lines and are usedin spectrometers to make precise measurements of light wavelengths.

When light reflects off the two surfaces of a thin film, an interference pattern isformed. This phenomenon is known as thin film interference. A thin coating is applied tolenses to make them nonreflective. For the coating to be nonreflective to light of

wavelength , the minimum thickness tof the coating is given by the equation:

t=

4n

where n is the refractive index of the lens glass. When a curved lens is placed on a flatglass plate, the wedge of air that is trapped between the two produces an interferencepattern consisting of concentric bright and dark circular fringes known as Newtons rings.

Light Geometric Optics Key Concepts

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