Optics for JEE (Main & Advanced)

362 Pages·2017·17.82 MB·English

by  Er. Anurag Mishra

BaJaJi
for
JEE
Main & Advanced
by:
Er. Anurag Mishra
B.Tech (Mech. Engg.)
HBTI Kanpur
5HRI BALAJI PUBLICATIONS
(EDUCATIONAL PUBLISHERS & DISTRIBUTORS)
[ANISO9001-2008 CERTIFIED OFtGANIZATIQNl
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IJ Published by: t
5HRI BAUUI PUBLICATIONS
(EDUCATiaNAL PUBLISHERS & DISTRIBUTORS)
[AN ISO 9001-2008 CERTIFIED ORGANIZATION]
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Jansath Road. Muzaffarnagar (U.P.)
:2L;
Phone :[phone] (O).2600503 (R)
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email: [email protected]
M First edition : 2011
U Third edition : 2013
11 Reprint : 2017
U ©Ali rights reserved withauthor
11 Price : ^ 250.00
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9! Printed at:
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All the rightsreserved. Nopartofthis publication
maybe reproduced, stored In a retrieval system
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Preface
Myinteractionwithstudents,sincerelypreparingforIIT-JEEmotivated
metowritethisbookonOptics.
Opticsisalsoanimportantpartofphysics Likemyotherbooks. "Optics
forIIT-JEE"isdesignedtocleartheconceptsthroughnumericalapproach.
This^bookwillhelpthe studentsinbuildinganalyticaland quantitative
skills,addressingkeymisconceptionsanddevelopingconfidenceinsolving
theproblems.
I sincerely wish that this book will fulfill all the aspirations of-the,
readers. Although utmostcare has beentakento make the bookfree'from
errors butsome errors inadvertently may creep in.Author and Publisher
shall be highlyobliged ifsuggestions regarding improvement and errors
are pointed"outlby readers. Iam indebted Neeraj Ji for providing me an
opportunitytowriteabookofthismagnitude.
I am indebted to my father Sh. Bhavesh Mishra, my mother Smt.
Priyamvada Mishra, my wife Manjari, my sister Parul, my little kids
Vrishank andIraforgivingtheir valuable timewhich Iutilizedduringthe
writing of this book and people of Moradabad, who supported me
throughoutmycareer.
I am also thankful to Mr. T. Kondala Rao, Mr. Abhishek Sinha
(Kanchi),Mr. Sunil Manohar, Mr. S.P. Sharma, Mr. SudhirSharma and
Mi^P. Narendra Reddy for their valuable suggestions in improving the
book.
Inthelast, Ialso pay mysincerethanksto alltheesteemedmembers of
ShriBalajiPublicationsinbringingoutthisbookinthepresentform.
AnuragMishra

How toface the challenge ?
Followingaresomedoubtswhichariseinthemindofalmostallthestudents
butmayface thembytakingsomecare.
1. / can notsolve numericalbecausemyconceptsarenotclear.Infactnumerical
solvingitselfisan exercisetolearnconcepts.
2. I can not study because I am in depression, Ifell into it because I was not
studying] Depressionis escapemechanismofpeopleafraidoffacing failures.
Failureisintegralpartoflearning.
3. Iunderstandeverythinginclassbutcan notsolveonmyown.WRlTlNGworkis
vital. It is a multiple activity, initially idea comes in mind then we put into
languageto expressit,wearefocussed in hand eye coordination,eyes create
visual impression on brain which is recorded there. WRITING WORKSARE
EMBOSSEDONBRAINLIKECARVINGSOFAJANTACAVES.
4. In examsmybraingoesblank, butIcan crackthem athome. Home attemptis
yoursecond attempt! you are contemplatingabout it while home back. You
do not behave differently in exam you replicate your instincts. Once a fast
bowler was bowling no balls. His coach placed a stump on crease, in fear of
(cid:127) injuryhegotitright.CONCEPTUALIZATION,WRITINGEQUATION,SOLVING,
THENPROBLEMGETSTOCONCLUSION!
/ am an averagestudent. It is a rationalization used bypeople afraid ofhard
work. In their reference frame Newton's first law applies "if 1 have a
misconception I will continue with it unless pushed by an external agent
even 1 will surround him in my web of misconception yielding zero
resultant."AVERAGEIS NOTDUETO CAPACITYLACUANEBUTDUETO LACK
OFDETERMINATIONTOSHEDINERTNESS.
Afamous cliche"I donothave luckin myfavour'' PRINCIPLE OFCAUSALITY:
CAUSE OF AN EVENT OCCURS IN TIME BEFORE OCCURRENCE OF THAT
EVENTi.e., causeoccursfirsttheneventoccurs.SHININGOF LUCKISNOTAN
INSTANTANEOUS EVENT IT IS PRECEDED BY RELENTLESS HARD WORK.
Sowaseedofaspirationinmind,wateritwithpassion,dedicationitwillbear
fruit,luckcangiveyousweeterfruit.
yL
I Useful tips:
I
I 1. Do nottake study asa burden actuallyitsaskilllikesingingand dancing. It
/ hastobehonedbyproperdevotionanddedication.
2. Without strong sense of achievement you can't excel. Before entering the
competitive field strong counselling by parents is must. Majority do not
know what for they are here. Nostrategic planning, they behave likea tail
enderbattinginfrontofSteyn'sbouncers.
3. Science is not a subject based on well laid down procedures or based on
learning some facts, it involves very intuitive and exploratory approach.
Unlesstheirisdesire and passionto learnyou cannotdiscover newideas. It
requirespatienceandhardwork,whosefruitsmaybetangiblelateron.
4. Somestudentsrealizeverylatethattheyarestudyingforacquiringskillsand
honingthem.Theirisafeeling thattheycan rideatthebackofinstructorand
achieve excellence.Studycomesas torturous exerciseenforcedon themand
theiris somemechanismthatcantakethisburdenofthem.
5. Scienceisnotaboutgaininggoodmarks,uptoXthbyreadingkeypointsgood
marks are achieved but beyond that only those survive who have genuine
interestinlearningandexploring.Selfstudyhabitismust.
6. IFYOUWANT TOGAIN LEAD START EARLY. Majorityofsuccessfulstudents
try to finish major portion elementary part of syllabus before they enter
CoachingInstitute. Dueto this their maturitylevelas compared to others is
more they get ample time to adjust with the fast pace. They are less
traumatizedbythe scientific matterhanded over. Forthose who enterfresh
' ' must be counselled to not get bullied by early starters but work harder
initiallywithinfirsttwo monthsinitialedgeisneutralized.
^ 7. Once astudent lags behindduetosomeforced orunforcederrors hismind
\ beginstoplayrationalizationremarkslike1amanaveragestudent,mymind
\ isnotsharpenough, Ihave lowIQetc.Thesewords aremechanisms used to
' \ avoidhardwork. Thesewordsare relativetermsapersonwho has earlystart
*\ maybeintelligentrelativetoyou.
Intelligence means-cumulative result ofhard work ofprevious years, that
hard work has eventuallyled to a development ofinstinct to crack things
I
\
easily.
Geometrical Optics
Optics(1); Natureoflight(1); Rectilinearpropagationoflight(2); Regularreflection(5);Theformation
of images by a plane mirror (7); Object (7); Image (8); Image formation from a plane surface (9);
,Vectorform oflawofreflection (9); Comerreflector (10); Angle ofdeviation (14); Extended object
(15); Number ofimages formed bytwo inclined plane mirrors (19); Spherical mirrors (27); Relation
^between focal length and radius ofcurvature (29); Raydiagram for concaye mirror(31); Velocityof^
imageinspherical mirror(36); Refraction(46); Huygen'sprinciple(50); Reversibilityoflightrays(50);
Partial reflection and partial refraction at the boundary of two media (55); Glass slab (58); Total
internal reflection and critical angle (61); Some explanation ofsome refraction phenomenon (63);
Optical fibre./Optical pipe (68); Variable refractive Index (74); Dispersion (86); Single surface
refraction equation (102); Thin lenses (109); Optical (111); Important points (114); Optional (116);
Analysis of graphs (118); Displacement method (123); Methods for determining focal length of a
convex lens (129);, Optical instruments (163); Simple microscope (166); Compound microscope
. (.167);Photometry(171);Subjectiveproblems(176);
Level-1: OnlyoneaItemativeiscorrect(187);Solution(206).
Level-2; Morethanonealternativeis/arecorrect(222);Solutions(224).
Level-3; Comprehension based problems (226); Matching type problems (231); Assertion and
reason(234);Solutions(237).
Wave Optics
Interference of light waves (244); Young's double slit experiment (248); Displacement of fringes
(253); Fresnel's mirrors (263); The interference condition by division of wave front and amplitude
(265); Billet's lens (266); Fringes of equal thickness (284); Newton's rings (285); Diffraction (288);
LimitOfresblutidri(292),Polarization(294);Subjectiveproblems(297);
Level-1: Onlyonealternativeiscorrect(307);Solutions(311)
Level-2: Morethanonealternativeis/arecorrect(315);Solution(317)
Level-3: Comprehension based problems (319); Matching type problems (322); Assertion and
reason(323);Solutions(325).
Previous Year Problems
Gr^^n
Vencal
seal?
dys
Otjecta? ^
GEOMETRICAL OPTICS
OPTICS
Optics is the branch of physics ±at studies the
phenomena and laws associated with the generation,
propagation, and interaction with a substance of
electromagnetic light waves. Light waves occupy an
enormous range on the scaleofelectromagneticwaves. It is (a) (c)
after the ultrashort millimetre radio waves and extends up
to the shortest electromagnetic waves known at present-
t- T •'t
gammarayswith awavelengthX,lessthanone angstrom(A) •^c
aA= 10"^°m).
Geometrical (ray) optics treats the laws of (b)
propagation of light in transparent media on the basis of
Fig.1.1
notions of light as a combination of light rays-lines along I-
which the energyoflight electromagneticwaves propagates. When the light contains a single wavelength it iscalled
Geometrical optics does not take into consideration the monochromatic (literally 'one colour'). On each of the
wave properties of light and the diffraction phenomena sheets the electric field has constant magnitude, it oscillates
associated with them. For instance, when light passes between to -^min we move from sheet to sheet. A
through a> lens with a mount diameter of d > X, given sheet moves to the right at the speed of light. The
where Xis the length of the light wave, we may electric field is different in planes located at different
ignore the diffraction at the edges ofthe lens. positions along the propagationdirection. Forsimplicitywe
take a particular sheet over which the electric field has a
NATURE OF LIGHT
particular phase of oscillation; e.g., we choose the phase
Lightisa transverse electromagneticwave. Lightwaves
where E has maximum value and is pointed upward. The
spread out in space in three dimensions; this makes
rectangular sheets of Fig. 1.1 (b) represent a wavefront,
visualization and representation of wave difficult. Fig. 1.1
on each of them the wave has an equivalentphase. Whenwe
(a) shows representation of simplest light wave, a
move from sheet to sheet, the phase increases or decreases
monochromatic plane wave.
by 2k rad. Figs. 1.1 (c) and (d) show spherical and
cylindrical wavefronts.
:i
Wavefronts travelwith the speed oflight. The direction Beams of light rays upon intersecting do not- interfere
ofenergy flow is given by PoyntingvectorAline tracing and propagate independentiy of each other after
theflow ofradiantenergy throughspace iscalleda ray. In an intersection.
isotropic medium rays are perpendicular to wavefronts. We
Ifa piece ofwood, tissue paper and glass, etc., are held
assume that the direction of motion of light is represented
in succession to a source of light, it is seen that some
by rays. Rays do not travel; they actually indicate paths of
substancesallowno lightto pass throughthem, whilstother
light. In the ray approximation we assumethata wave
substances do so to varying degrees. Hence we apply the
through a medium travels in a straight line in the direction
terms —
of its rays.
opaque, to substances which allow no light to
1. Parallel rays indicate plane wavefronts. pass tiu'ough them,
2. Diverging rays indicate expanding wavefronts.
transparent, to substances which allow much
3. Converging rays indicate collapsingwavefronts. light to pass through them,
When a wave meets an obstacle with circular opening translucent, to substances which allow a
whose diameter is much larger than the wavelength, the smaller portion.oflight, falling on them (or as we
wave emerging-from the opening continues to move in a say, incident upon them), to pass through.
straight line, hence the ray approximation is'valid. If the
The light which passes through is called
diameter of the opening is of the order of the wavelength transmitted light. But what happens to the light falling
[Fig.1.2 (b)].the waves^spread out fromsthe opening in all
on an opaque body ? Since fiie body is visible it must
directions. ^ ^^^ ^ . throw off, or reflect, light just as a wall or floor
throws off, orreflects, a ballthrown on it. Butthere
is a difference, forwhereas a ballisonlyreflected in theone
direction, light must be reflected in all directions. An
object (C^ be seen., ifrom^ parts of a room,
despitethe fact that onlya singlesourceoflightis
illuminating it. This process by which. a body
reflects incident light in all directions is called
X«d irregular or disuse reflection or scattering, of
X»d
light, and it is due to this process that we
ordinarily,see objects.
Fig.1.2
RECTILINEAR PROPAGATION OF LjGHT
Finally, if the opening is much" smaller than the
wavelength/the opening can be approximated as a point Light Rays ' .vv./-! '" r'' . mv
source-ofwaves,"eachincidentlightraysubsequentlytravels _ 1 . ( . •
Observations show that in homogeneous media, light
in a unique direction. Well defined shadows exist'ihregions also propagates, along s^traight lines. When an object is
wherethere,arenorays..Whenawaveencountersahobject
of dimensions d arid if X« d, the object casts^a sharp
shadow. In'this'chapter'the ray apprb>dmatibn'and die
assumption that X« dhave been used.
A medium is
defined as optically
homogeneous if its
refractive index is
everywhere . the
same. In an optically
homogeneous . . .
medium, the rays are
Fig.1.3
straight: in .such .a , , . . .
medium light propagates rectUinearly. This
IS Fig:1.4:When-a point source's illuminates
confirmedbydieformationofshadows. If5isapointsource
a pjane object O parallel to a screen,
of light, and K is.a body in the.path of the light from the asharpshadow(umb/a)O'formed on i
source, then a cone of a shadowis,formed beyond the body thescreenIssimilaf.totheobject. •,
K (Fig. 1.3).Noipointinsidethis conereceivesTightfromthe
source.Awell-definedshadowofthebodyKisobtainedon a illuminatedbyapoint soturce,asfiarp shadow (umbra)
screen placed at right angles to the axis ofthe cone. isformed (Fig.1.4),whose shape issimilarto the shape of a