IIT-JEE Super Course in Physics - Vol 5 Optics and Modern Physics

230 Pages·2011·10.196 MB·English

by  Trishna Knowledge Systems

Super Course in Physics
OPTICS AND
MODERN PHYSICS
for the IIT-JEE
Volume 5
Trishna Knowledge Systems
A division of
Triumphant Institute of Management Education Pvt. Ltd
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Contents
Preface iv
Chapter 1 Optics 1.1—1.135
sTUDY MATERIAL
• Introduction • Reflection  • Refraction • Prisms • Refraction at Spherical
Surfaces • Lenses • Optical Instruments (For Additional Reading) • Wave Optics
Interference • For Additional Reading
Chapter 2 Modern Physics 2.1—2.89
STUDY MATERIAL
• Electromagnetic Waves • Photons • Electromagnetic Spectrum • The Photoelectric
Effect • Matter Waves • Bohr Theory • X-Rays • Nuclear Physics • Radioactivity
Preface
The IIT-JEE, the most challenging amongst national level engineering entrance examinations, remains on the top of the
priority list of several lakhs of students every year. The brand value of the IITs attracts more and more students every year,
but the challenge posed by the IIT-JEE ensures that only the best of the aspirants get into the IITs. Students require thorough
understanding of the fundamental concepts, reasoning skills, ability to comprehend the presented situation and exceptional
problem-solving skills to come on top in this highly demanding entrance examination.
The pattern of the IIT-JEE has been changing over the years. Hence an aspiring student requires a step-by-step study
plan to master the fundamentals and to get adequate practice in the various types of questions that have appeared in the
IIT-JEE over the last several years. Irrespective of the branch of engineering study the student chooses later, it is important
to have a sound conceptual grounding in Mathematics, Physics and Chemistry. A lack of proper understanding of these
subjects limits the capacity of students to solve complex problems thereby lessening his/her chances of making it to the top-
notch institutes which provide quality training.
This series of books serves as a source of learning that goes beyond the school curriculum of Class XI and Class XII
and is intended to form the backbone of the preparation of an aspiring student. These books have been designed with the
objective of guiding an aspirant to his/her goal in a clearly defined step-by-step approach.
• Master the Concepts and Concept Strands!
This series covers all the concepts in the latest IIT-JEE syllabus by segregating them into appropriate units. The theories
are explained in detail and are illustrated using solved examples detailing the different applications of the concepts.
• Let us First Solve the Examples—Concept Connectors!
At the end of the theory content in each unit, a good number of “Solved Examples” are provided and they are designed
to give the aspirant a comprehensive exposure to the application of the concepts at the problem-solving level.
• Do Your Exercise—Daily!
Over 200 unsolved problems are presented for practice at the end of every chapter. Hints and solutions for the same are
also provided. These problems are designed to sharpen the aspirant’s problem-solving skills in a step-by-step manner.
• Remember, Practice Makes You Perfect!
We recommend you work out ALL the problems on your own – both solved and unsolved – to enhance the effective-
ness of your preparation.
A distinct feature of this series is that unlike most other reference books in the market, this is not authored by an in-
dividual. It is put together by a team of highly qualified faculty members that includes IITians, PhDs etc from some of the
best institutes in India and abroad. This team of academic experts has vast experience in teaching the fundamentals and
their application and in developing high quality study material for IIT-JEE at T.I.M.E. (Triumphant Institute of Manage-
ment Education Pvt. Ltd), the number 1 coaching institute in India. The essence of the combined knowledge of such an
experienced team is what is presented in this self-preparatory series. While the contents of these books have been organized
keeping in mind the specific requirements of IIT-JEE, we are sure that you will find these useful in your preparation for
various other engineering entrance exams also.
We wish you the very best!
c h a p t e r Optics
1
nnn Chapter Outline
Preview
sTUDY MATERIAL TOPIC gRIP
• subjective Questions (10)
Introduction
• straight Objective Type Questions (5)
Reflection
• Assertion–Reason Type Questions (5)
• Concept strands (1-4)
• Linked Comprehension Type Questions (6)
Refraction • Multiple Correct Objective Type Questions (3)
• Concept strands (5-16) • Matrix-Match Type Question (1)
Prisms
IIT AssIgnMEnT ExERCIsE
• Concept strands (17-22)
• straight Objective Type Questions (80)
Refraction at spherical surfaces
• Assertion–Reason Type Questions (3)
• Concept strands (23-25)
• Linked Comprehension Type Questions (3)
Lenses • Multiple Correct Objective Type Questions (3)
• Concept strands (26-37) • Matrix-Match Type Question (1)
Optical Instruments (For Additional Reading)
ADDITIOnAL PRACTICE ExERCIsE
• Concept strands (38-41)
• subjective Questions (10)
Wave Optics
• straight Objective Type Questions (40)
Interference • Assertion–Reason Type Questions (10)
• Concept strands (42-50) • Linked Comprehension Type Questions (9)
For Additional Reading • Multiple Correct Objective Type Questions (8)
• Concept strands (51-52) • Matrix-Match Type Questions (3)
COnCEPT COnnECTORs
• 26 Connectors
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Optics 1.3
intrOduCtiOn
Optics is the branch of Physics, which deals with the na-
ture, sources, properties and effects of light. Optics is clas-
sified into Geometrical Optics (also called Ray optics) and
Physical Optics (or Wave Optics).
Geometrical optics is the study of simple properties of
light and optical instruments assuming rectilinear propa-
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gation of light (i.e., light travels in straight lines). (cid:69)(cid:72)(cid:68)(cid:80)(cid:3) (cid:69)(cid:72)(cid:68)(cid:80)(cid:3) (cid:69)(cid:72)(cid:68)(cid:80)(cid:3)
Optical medium is one through which light can pass.
It may or may not contain matter.
Fig. 1.1
Transparent medium is one through which most of
the incident light passes.
Translucent medium is one through which only a If the physical properties of a medium are different in
small portion of the incident light passes. different directions, it is called an anisotropic medium.
Opaque medium is one through which no light can These are usually crystalline materials. Example, quartz,
pass. calcite. In these media, light travels with different speeds in
A ray or ray of light is the straight line, which repre- different directions.
sents the direction of propagation of light. The point where the light rays coming from a
A collection of rays of light is called a beam of light. A source meet or appear to diverge from, after undergoing
beam of light could be converging (meeting at a point), di- reflection, refraction or both, is called the image point of
verging (emanating from a point) or parallel. See Fig. 1.1. the source.
A medium that has same composition of matter If the rays actually converge or meet at a point after
throughout (hence the same density at all points) is called a reflection/refraction, the image is real and it can be caught
homogeneous medium. on a screen. Real images of real objects are inverted.
A medium having the same physical properties in all If the rays appear to diverge from a point, after reflec-
directions is called an isotropic medium. Light travels with tion, refraction, that point is the virtual image point of the
the same speed in all directions in an isotropic medium. source. It cannot be caught on a screen. Virtual images of
Example, glass. real objects are erect.
refleCtiOn
When light travelling The reflecting surface is called a mirror or reflector,
Incident ray
in one medium (called which can be either a plane surface (called plane mirror) or
A
incident medium), rea- a curved surface (called spherical, ellipsoidal or parabolic
ches the boundary with mirrors depending upon the shape of the curved surface).
another medium and Fig. 1.2 illustrates reflection at a plane mirror.
g
the bounding surface i
throws the incident N O O = Point of incidence
Normal r
light partly or wholly ON = Normal to the point of incidence
back into the incident
AO = Incident ray
medium, the phenome-
OB = Reflected ray
non of reflection is said
to have taken place at Reflected ray i = Angle of incidence
the boundary separat- B
r = Angle of reflection
ing the two media. Thus Fig. 1.2
g = Glancing angle
reflection is a boundary
phenomenon. = 90° - i
1.4 Optics
The angle which the incident ray makes with the nor- The point to which incident rays appear to converge is
mal at the point of incidence is called angle of incidence (i) called a virtual object (O’). See Fig. 1.4.
The angle which the reflected ray makes with the normal at
the point of incidence is called angle of reflection (r). The
angle which the incident ray makes with the plane reflect-
ing surface is called glancing angle (g).
g = 90° - i
O’
laws of reflection
(i) The incident ray, the reflected ray and the normal at
the point of incidence, all lie in the same plane.
(ii) The angle of incidence (i) is equal to the angle of reflec-
Fig. 1.4
tion (r) i.e., i = r.
The above laws hold good for all reflecting surfaces,
whether plane or curved.
note:
notes: Virtual object and incident rays will be on the opposite
sides of the reflecting (or refracting) surface. See Fig. 1.4.
(1) If ∠i = 0, the ray is incident normally on the reflecting
surface. For normal incidence, ∠r = 0 as per laws of
reflection. Hence for i = 0 (normal incidence), the ray real image and virtual image
retraces its path after reflection.
(2) Since the incident ray and reflected ray travel through The point to which reflected or refracted rays actually con-
the same medium, there is no change in the frequency, verge is called a real image (I) point. See Fig. 1.5.
wavelength and speed of the ray after reflection.
(3) The intensity of the reflected ray may be less than the
intensity of the incident ray due to the decrease in the
amplitude. [Q Intensity m (amplitude)2]. Ι
(4) If a parallel beam of light is incident on an irregular
reflecting surface, the light rays are reflected in random
directions but for each ray, laws of reflection can be
applied. Such a reflection is called irregular reflection
Fig. 1.5
or diffuse reflection.
real object and virtual object
note:
Real image and the reflected (or refracted) rays towards it
A point object from which incident rays actually diverge is
will be on the same side of reflecting (or refracting) surface.
called a real object (O).
The point from which reflected rays (or refracted rays)
appear to diverge is called a virtual image ( I’ ) point. See
note:
Fig. 1.6.
Real object and incident rays from it will be on the same
side of the reflecting (or refracting) surface. See Fig. 1.3.
I’
O
Fig. 1.3 Fig. 1.6
Optics 1.5
note: By elementary geometry, it can be proved that OO’ = II’
Virtual image and the reflected (or refracted) rays will be on
imagedimension
the opposite sides of the reflecting (or refracting) surface. Lateral magnification m = = 1
objectdimension
reflection from plane mirror (In this case dimension is length or height).
(image formation) By elementary geometry, we can show that
Two rays are sufficient to locate the image of a point ob-
m = 1.
ject by reflection. As shown in Fig. 1.7, we take one ray at
normal incidence, i.e., i = 0, and another at any arbitrary If the object OO’ is perpendicular to the surface of the
i emanating from the point object O as shown. The one mirror as shown in Fig. 1.9, we can show easily that the im-
which is at normal incidence is reflected back along the line age II’ is also perpendicular to the surface of the mirror and
of incidence, but the ray which is incident at angle i is re- the longitudinal magnification,
flected at an angle i. They do not meet in front of the mirror. m’ = -1.
But the ray at angle i, when extended behind the mirror,
meets the extension of the normal ray at a point I, which is
the virtual image of O.
O' O I I’
i
i
Ι
O
Fig. 1.9
x y
Fig. 1.7
If the object is a plane area as shown in Fig 1.10, the
image formed behind the mirror can be seen to be laterally
Consider reflection at a plane mirror as shown in inverted. Image of the left hand looks like the right hand.
Fig. 1.8. The object is at a distance x and image is at a dis-
tance y. By the properties of congruent triangles, we can
prove x = y. Now consider an extended object OO’ such that
it is parallel to the surface of the mirror. The point O’ is at
the same object distance x. The image of O’ is I’ at same y.
Image of the object OO’ is therefore II’, as shown in Fig. 1.8. Virtual image
(An infinite number of point objects between O and O’ will
have their corresponding point images between I and I’)
Real Object Mirror
Fig. 1.10
O’ Ι’
O Ι
Image formed by plane mirrors kept inclined at an
x y angle (q)
Fig. 1.8 Consider two plane mirrors kept inclined to each other at
an angle q, with their reflecting surfaces facing each other.