Introduction Light is a form of energy, which helps us to perceive things, using our visual sense. Yet, what light actually is, is a question that has concerned scientist, over the years. Though it may seem perplex, yet light actually has a dual nature, of wave, as well as of particle!! Seems weird ?? Well lets find out…. Light - The Tutorial 2
In this Tutorial you’lllearn about… What actually is light ? How light propagates ? How does reflection and refraction occur ? How does spherical mirrors and lenses, actually work ? How can light energy, be harnessed for good ?
On a whole we shallconceptualize… 1) Nature of light. 2) Theories put forward on propagation of light. 3) Reflection & refraction at plane surfaces, using wave theory of light. Light - The Tutorial 4
Also focusing on…… 4) Spherical mirrors and lenses – How do they work 5) Efficient utilization of light energy for the betterment of mankind.
Light – A Big Picture Initially many theories were put forward to the nature of light. Newton in 1675, formulated that light was made of small particles called corpuscles, which fly off in space in all directions. Huygens in 1678,suggested that light consists of periodic disturbances that are transmitted through the medium in the form of waves. The Huygens theory, though could explain the geometrical optics, but could not explain phenomenon like interference, diffraction etc. Light - The Tutorial 6
Light – A Big Picture To overcome this anomaly, Maxwell suggested the modern electromagnetic theory of light. Maxwell’s equation forms the basis of modern optics still today, though other theories like the quantum theory has been proposed. Lets find out a little more about Maxwell….
Maxwell’s Equations Everywhere there was darkness. Then God said: ∇⋅ E = 4πρ And there was light! 4π 1 ∂E Well, actually, it= Scottish physicist ∇× B was J + James Clerk Maxwell in 1865, ∂t those c c and 1 ∂B were Maxwells equations!! ∇× E + =0 c ∂t Seems weird ?? May be !!!! ∇⋅ B = 0
Maxwell’s EquationsAccording to Maxwell, light is a wave withoscillating electric and magnetic fieldsperpendicular to each other. Today, we call these disturbances “electromagnetic radiation.”
Wavelength A wave must have a unit to measure its length. The wavelength, l, is the distance from one wavecrest to the next. The wavelength determines the color of the light.
Electromagnetic SpectrumAs wave length changes,so changes the colors andother characters of light.
Eye Sensitivity toHowever our Coloreyes perceivesthe sense ofeach color to avarying degree,and issensitive themost to green.
Reflection Reflection means the retracting back of light rays, on hitting a surface. Reflection off a flat surface follows a simple rule: Angle in (incidence) equals angle out Angles are measured from surface “normal” (perpendicular). surface normal same exit ray incident ray angle
Reflection, continued…. Also consistent with “principle of least time” : Light rays must follow the shortest path, so as to reach the destination point in least time. If going from point A to point B, reflecting off a mirror, the path traveled is also the most expedient (shortest) route A shortest path; too long equal angles B
Hall Mirror Useful to think in terms of images“real” you mirror only needs to be half as “image” you high as you are tall. Your image will be twice as far from you as the mirror.
Plane mirrors Real side Virtual side Angle of incidence i=-p Normal Virtual imageAngle of reflection
Curved mirrors What if mirror isn’t flat? still follows same rules, with local surface normal Parabolic mirrors have exact focus. used in telescopes, backyard satellite dishes, etc. also forms virtual image
Questions What is light? What are the different theories on nature of light? What are their success and drawbacks ? How are they different ? How does light propagate? What is reflection and how does it occur? How come curved mirror follow the laws of reflection ?
Refraction Light also goes through some things glass, water, eyeball, air However, light bends or deviates from its normal path, due to change in velocity, on moving from a denser to a rarer medium or vice versa. This phenomenon is called refraction. Light slowing factor called index of refraction glass has n = 1.52, meaning that light travels about 1.5 times slower in glass than in vacuum water has n = 1.33 air has n = 1.00028 vacuum is n = 1.00000 (speed of light at full capacity)
Refraction at a plane surface Light bends at interface between refractive indices bends more the larger the difference in refractive index can be effectively viewed as a “least time” behavior get from A to B faster if you spend less time in the slow medium
Refraction continued…... A Experts only: θ1 n1sinθ1 = n2sinθ2 n1 = 1.0 n2 = 1.5 θ2 B
Refraction separates colors….As different constituent colours of white light gets refractedto different degrees, we see a split up of white light,through a prism.
Total Internal Reflection At critical angle, refraction no longer occurs thereafter, you get total internal reflection for glass, the critical internal angle is 42° for water, it’s 49° a ray within the higher index medium cannot escape at shallower angles (look at sky from underwater…)
Total Internal Reflection…. incoming ray hugs surface n1 = 1.0 n2 = 1.5 42°
Reflection and Refraction θ= 1 1 θ Snells Law n1 nn=sθ 1 θ nn s 1 2i 2 i n2
Reflections, Refractive offset associated with it Let’s consider a thick piece of glass (n = 1.5), and the light paths reflection fraction = [(n1 – n2)/(n1 + n2)]2 using n1 = 1.5, n2 = 1.0 (air), R = (0.5/2.5)2 = 0.04 = 4% n1 = 1.5 n2 = 1.0incoming ray (100%) image looks displaced due to jog 96%8% reflected in tworeflections (front & back) 4% 92% transmitted 4% 0.16%
Questions What do you think you would see from underwater looking up at sky? Why do the sides of aquariums look like mirrors from the front, but like ordinary glass from the sides? If you want to spear a fish from above the water, should you aim high, right at the fish, or aim low (assume fish won’t move)?
We know… That for mirrors the following incident occurs….
i=-p magnification = 1What happens if we bend the mirror? Concave mirror. Image gets magnified. Field of view is diminished Convex mirror. Image is reduced. Field of view increased.
Just as with mirrors, curved lenses follow same rules as flat interfaces, using local surface normal A lens, with front and back curved surfaces, bends light twice, each diverting incoming ray towards centerline. Follows laws of refraction at each surface. Parallel rays, coming, for instance from a specific direction (like a distant bird) are focused by a convex (positive) lens to a focal point. Placing film at this point would record an image of the distant bird at a very specific spot on the film. Lenses map incoming angles into positions in the focal plane.
Types of lenses: Lense s• Most important simple optical device• Lenses form images of objects• Used in glasses, cameras, telescopes,binoculars, microscopes, …• Converging lenses: thicker in themiddle than the outside• Diverging lenses: Thinner in themiddle than the outside
Parallel rays incident on converging lens Converging lens• Light rays get refracted by lens, thatis: light gets bend by a lens.• If the rays come in parallel to theprincipal axis (object at infinity), theywill be focused in the focal point.• focal length f• focal length is the same on bothsides, even if lens is not symmetric. Parallel rays coming in focus on the focal plane
Parallel rays incident on converging and diverging lenses• Any lens that is thicker in thecenter than at the edges will makeparallel rays converge to a pointand is called a converging lens.• Any lenses that are thinner in thecenter are called diverging lenses,because they make parallel raysdiverge.• Focal point of diverging lens:Point were diverging rays seem tobe coming from.
Converging Lenses to bend light rays A converging lens uses refraction Light rays converge after passing a converging lens Rays from a common point on an object converge to a common point on far side of the converging lens
Real Images An image forms in space on far side of the lens The image is a pattern of light in space that exactly resembles the object, except for size and orientation The image is “real” – you can put your hand in it and you can capture it on a screen.
Lenses and Film Film records the pattern of light it’s exposed to Eyes image, it will record a If you put film in a real and Retina pattern of light resembling the object For a good photograph, the real image should be sharply focused on the film and have the right size Film or retina
Focusing Light reaching the lens from an object is diverging The nearer the object, the more its light diverges Converging lens has trouble with diverging light Real image of nearby object forms farther from lens Real image of distant object forms closer to lens 1 1 1 + = Object distance Image distance Focal length
Focal Length Focal length measures the lens’ converging ability Long focal length: weak convergence, long image distance Short focal length: strong convergence, short image distance The larger the object distance, the bigger the image Long focal length: big images Short focal length: small images
Ray tracing for converging lens to find the image created by the lens (a) Ray 1 leaves top point on object going parallel to the axis, then goes through focal point. (b) Ray 2 passes through F’, therefore it is parallel to the axis beyond the lens (c) Ray 3 passes straight through the center of the lens.
1 1 1The lens equation: + = o i f hi i Magnification: m= =− ho o1. Draw a ray diagram2. Solve for unknowns in the lens equation and magnification. Remember reciprocals3. The height of the image, hi is positive if the image is upright, and negative if the image is inverted relative to the object (h o is always positive).
Exampl eImage formed by a converging lens.What is the (a) position and (b) size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal lens camera?ho =7.6 cm hi f = 5 cm o = 100 cm i=?
Lens Diameter Larger lens converges more light brighter image focus becomes more critical less depth of focus Smaller lens dimmer image focus becomes less critical more depth of focus
Aperture and f-number Aperture characterizes the diameter of the lens F-number is lens focal length (say 35 mm) divided by lens diameter (adjusted by aperture). Large f-number (22 or so on lens). Dim image Large depth of field/focus (focus is forgiving) Small f-number (3.5 or so on lens). Bright image Small depth of field/focus (focus is critical)
Cameras and Projectors Cameras and projectors work the same way: transfer an image from one plane to another projector translates “film” plane to screen plane camera translates direction into position on film pinhole camera is simplest approach, but low throughput
Telescopes Telescopes do two things: collect a lot of light across a big aperture (opening) and cram this light into your eye magnify angles by ratio of the focal lengths of the main lens/mirror and eyepiece Come in two generic varieties: refractors, dating back to Galileo’s time (saw moons of Jupiter) reflectors, invented by Newton! all big telescopes are reflectors
The Eye Now for our cameras… Eye forms image on retina, where light is sensed Cornea does 80% of the work, with the lens providing slight tweaks (accommodation, or Refractive indices: adjusting) air: 1.0 cornea: 1.376 fluid: 1.336 lens: 1.396 Central field of view (called fovea) densely plastered with receptors for high resolution & acuity. Fovea only a few degrees across.
Questions Why are contacts and corneal surgery (e.g., radial keratotomy) as effective as they are without messing with innards of eye? Why can’t we focus our eyes under water? Why do goggles help?
Problem: Two plane mirrors make an angle of90o. How many images are there for an objectplaced between them? mirror eye object 2 mirror 1 3
Thin Lenses: thickness is small compared to object distance, image distance, and radius of curvature.Converging lensDiverging lens
Lens Equation for thinLenses Thin Lens Equation Lens maker Equation 1 1 1 1 1 1 = + =(n− ) − ) 1( f p i f r r 1 2 What is the sign convention?
Sign Convention Virtual side - V Real side - R Light r1 r 2 p i Real object - distance p is pos on V side (Incident rays are diverging) Radius of curvature is pos on R side. Real image - distance is pos on R side.Virtual object - distance is neg on R side Incident rays areconverging)Radius of curvature is neg on the V side.Virtual image- distance is neg o the V side.
Rules for drawing rays to locate images•A ray initially parallel to the central axis will pass throughthe focal point.•A ray that initially passes through the focal point willemerge from the lens parallel to the central axis.•A ray that is directed towards the center of the lens willgo straight through the lens undeflected.
1. Given a lens with a focal length f = 5 cm and objectdistance p = +10 cm, find the following: i and m. Is the imagereal or virtual? Upright or inverted? Draw 3 rays. Virtual side Real side . F1 . p F2 1 1 1 = − y′ i i f p m= =− y p Image is real, inverted. 1 1 1 1 = − =+ 10 i 5 10 10 m=− =−1 10 i +c =0 1m
2. Given a lens with the properties (lengths in cm) r 1 = +30, r2= -30, p = +10, and n = 1.5, find the following: f, i and m. Isthe image real or virtual? Upright or inverted? Draw 3 rays. Virtual side Real side . F1 r2 p r1 . F2 1 1 1 1 1 1 y′ i = ( n − 1) − r r = − m= =− f i f p y p 1 2 1 1 1 1 1 1 1 1 −5 1 = (1.5 − 1) − = − =− m=− =+ .5 1 = 10 f 30 − 30 30 i 30 10 15 Image is virtual, f = 30cm i = −15cm upright.
3. A converging lens with a focal length of +20 cm islocated 10 cm to the left of a diverging lens having a focallength of -15 cm. If an object is located 40 cm to the leftof the converging lens, locate and describe completelythe final image formed by the diverging lens. Treat eachlens separately. Lens 1 Lens 2 +20 -15 f1 f2 f1 f2 40 10
Lens 1 Lens 2 +20 -15 f1 f 2 f1 f2 40 40 10 30 Ignoring the diverging lens (lens 2), the image formed by the converging lens (lens 1) is located at a distance1 1 1 1 1 This image now serves = − = − . i = 0m 1 4c as a virtual object fori f p 2c 4c1 1 1 0m 0m lens 2, with p2 = - (40Since m = -i1/p1= - 40/40= - 1 , the image is inverted cm - 10 cm) = - 30 cm.
Lens 1 Lens 2 +20 -15 f1 f2 f1 f2 40 40 10 30 The magnification is 1 1 1 1 1 = − = − i2 = 3 c . − 0m m = (-i1/p1) x (-i2/p2) i f2 p − 5m − 0m 1c 3c = (-40/40)x(30/-30) 2 2Thus, the image formed by lens 2 =+1, so the imageis located 30 cm to the left of lens has the same size2. It is virtual (since i2 < 0). orientation as the object
Efficient Utilization of lightto solve our energyproblems…. be converted to various useful Light energy can forms to meet our daily energy requirements. One method of doing so, is converting light energy to electrical form through the use of special converters, called solar cells. Since each solar cell can convert only a small fraction of light energy, so an array of cells are often used.
Solar Cell As light is a renewable sources of energy, so a wide usage of solar cell can help us to solve our problem of non renewable energy sources, and make the world a better place to live in.
SummarySo we learnt about : What is light, and its behavior. What are mirrors and how do they work. What are lenses and how do they work. How does a telescope work What are the ways of utilizing light energy for the betterment of mankind. Light - The Tutorial 66
Application & Feedback…. From now on, I hope you can understand yourself, how does the optical instruments around you work. Make effort to utilize light energy efficiently. How did you like this training session? Please give a feedback to your concerned teacher. Happy learning students……
You Can Get More Information from… Searching google.com on the internet. The Optics Book - by Sharon Levine, Leslie Johnstone The Scientific Papers of James Clerk Ma - by James Clerk Maxwell Optics and Lasers - by Matt Young Consulting your science teacher. Light - The Tutorial 68
Bibloigraphy The Optics Book - by Sharon Levine, Leslie Johnstone A complete course in ISC Physics – by Dr. V.P. Bhatnagar A Text book of Physics, by Chittaranjan Dasgupta The Internet.