Download Mindfiesta Page 1 CHAPTER – 10 WAVE OPTICS EXPERTS TIPS

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CHAPTER – 10
WAVE OPTICS
EXPERTS TIPS :
(1) Even in an irregular (or diffuse) reflection, the angle of incidence is equal to the angle of
reflection at each point of incidence.
(2) A plane mirror may be considered as a spherical mirror of infinite focal length.
(3) The image formed by a plane mirror is always erect, virtual, of same size, laterally
inverted and is located as far behind the mirror, as the object is in front of it.
(4) When a ray of light falls on a mirror normally, both the angle of incidence and the angle of
reflection are zero.
(5) The minimum size of the plane mirror, in which a person can see his full image, is equal
to half of his height.
(6) The spherical aberration in spherical mirrors arises, when their aperture is large. To avoid
spherical aberration, parabolic mirrors are used.
(7) When a concave / convex spherical mirror produces a virtual image :
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(a) The rays of light form the object only appear to come from the image.
(b)The image is always erect.
(c) The size of the image may be same / smaller / larger than the size of the object.
(d)The linear magnification is positive as the image formed is always erect.
(8) When a concave spherical mirror produces a real image :
(a) The rays of light from the object actually meet at the image.
(b)The image is always inverted.
(c) The size of the image may be the same / smaller / larger than the size of the object.
(d)The linear magnification is negative as the image formed is always inverted.
(9) The mirror formula holds for a spherical mirror of small aperture only.
(10) A convex mirror always produces a virtual image. However, if a beam of light from a
virtual object converges to a point behind the convex mirror, then its real image will be
formed in front of the mirror.
(11) In case of a convex mirror, always a virtual and diminished image is formed, irrespective
of the position of the object.
(12) The focal length of a spherical mirror remains the same, when
(a) The wavelength of light used is changed and,
(b)The mirror is placed inside a liquid.
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(13) The number of images of a point object placed between two plane mirrors
inclined at an angle ,
n = (360o/)-1, if 360o/ is an even integer and the object may or may not lie on
the bisector of the angle ;
n = (360o/)-1, if 360o/ is an odd integer and the object lies on the bisector of
the angle  and
n = 360o/,
if 360o/ is an odd integer and the object does not lie on the bisector of the
angle .
(14) If a vehicle is overtaking a car fitted with a driving mirror (convex mirror) of
focal length f, then the speed of the image of the vehicle formed by the mirror is
given byspeed of the image of the vehicle = 
f2
u  f 
2
 relative speed of the
vehicle w.r.t. the car,where u is the distance of the vehicle from the car.
(15) The parameters such as speed, frequency and wavelength of the light do not
change, when the light undergoes reflection.
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(16) The refraction index of a material in terms of the wavelength of the light is given
by
  a
b
c

2  4
(17) When light travels from one medium to anther, it gets refracted. The cause of refraction of
light is that it travels with different speeds in different refracting media.
(18) Snell’s law fails, when light is incident normally on a refracting medium.
(19) The absolute refractive index of a medium cannot be less than unity. It is because, the
velocity of light is maximum in vacuum (or air).
(20) When a convex lens produces real image, m is negative and when image formed is virtual,
m is positive
(21) The focal length and power of a spherical refracting surface of a lens depend upon the
refractive index of the surrounding medium also in addition to the refractive index of the
material and the radii of curvature of its two surfaces.
(22) When a glass lens is immersed in water, its focal length increases and hence its power
decreases.
(23) The power of a thick lens is greater than that of a thin lens.
(24) The focal length of a plane glass plate is infinite and its power is zero.
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(25) The image produced by a concave lens is always virtual and smaller in size.
(26) The power of a spherical refracting surface or a lens gives the measure of the degree to
which it can converge or diverge the rays of light passing through it.
(27) The lens equation and the mirror formula obtained by applying the new cartesian sign
conventions are not the same.
(28) The phenomenon of reflection and total internal reflection are different from each other in
the following respects :
(a) Whereas reflection can occur, when the incident ray travels inside a rarer or a denser
medium; the total internal reflection takes place only when the incident ray travels in
a denser medium and falls on the interface of the two media.
(b) Whereas reflection can occur at all the values of the angle of incidence; the total
internal reflection takes place only when the ray of light is incident at an angle of
incidence greater than the critical angle.
(c) Whereas 100% of incident light energy cannot be reflected through the phenomenon
of reflection, the entire light energy is reflected during the phenomenon of total
internal reflection.
(29) It may by noted that a lens forms the image on the other side of the real object; while the
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virtual image is formed on the same side the object. Therefore, in case of a lens, the
distance of the real image from the lens is taken as positive and that of virtual image is
taken as negative.
(30) The lateral shift produced by a parallel sided glass plate is
(a) zero, when the angle of incidence is 0o and,
(b) maximum (equal to the thickness of the refracting slab), when the angle of incidence
is 90o.
(31) When a glass-slab is placed over a page, over which letters are printed in different
colours, the image of the letters of different colours do not lie in the same plane.
It is because, the refractive index of the glass for red light (maximum wavelength) is
minimum and foe violet light (minimum wavelength) is maximum. Likewise, the normal
shift of the letters given by

1
d  t 1  


is maximum for letters in red colour and minimum for letters in violet colour. Therefore,
the red coloured letters appear more raised up.
(32) Out of the parameters such as speed, frequency and wavelength of the light, the speed
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and wavelength change, when the light undergoes refraction. The frequency of the light
remains the same.
(33) When a luminous object is placed at a depth d inside water (or any transparent medium)
an observer receives light from it in a cone of semivertical angle equal to the critical angle
for the water-air interface circular area disc is placed vertically above the object on the
surface of the glass-slab The radius of the circular base of the cone is given by
r = d tan C
(34) When light of wavelength  travelling in air at speed c enters a medium of refractive index
, its speed and wavelength decrease by a factor  i.e. becomes c/ and / respectively.
(35) According to lens maker’s formula, focal length of a lens is given by
1

f
 1
   1  R

1

1 

R2 
When a convex lens made of material of refractive index  is placed in a medium of
refractive ’, it behaves as
(a) it ceases to behave as a lens (f=  ), if ’ = .
(b) it still behaves as a converging lens (f=positive), if ’<.
(c) it behaves as a diverging lens (f=negative), if ’>.
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(36) According to lens maker’s formula, focal length of a lens is given by
1

f
 1
   1  R


1
1 

R2 
Since the refractive index of the material of a lens decreases with increase in wavelength
of incident light, it follows that focal length of the lens will increase with increase in
wavelength of incident light.
(37) An air bubble inside a transparent liquid behaves as a convex lens made of air and placed
inside the liquid. As such its focal length is given by
1
fbubble



a
 1
1 
1 


 R1 R 2 

Since  a  1 i.e.  a  1 is negative, the air bubble inside a transparent liquid behaves as a
diverging lens.
(38) A convex lens of focal length f produces an N times magnified image, when the object
distances from the lens have magnitude (f  f/N).
(39) When a lens is placed inside a liquid of refractive index   a , its focal length is given by
1
fliquid



1
1 

a  1 

 , where g 
 R1 R2 

a
g
a

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It follows that
(a) fliquid  fair . For example, when a convex lens made of glass ( a g  3 / 2 ) is
placed inside water ( a   4 / 3 ), its focal length inside water will become
four times its focal length in air.
(b) a concave lens will still behave as a converging lens, if a   ag . It is because,

g  1 .
(c) a convex lens will behave as a diverging lens, if a   ag . It is because,

g  1 .
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(40) When a convex lens produces a real image of an object, the minimum distance between
the object and the image is equal to four times its focal length.
It is because, the lens equation gives a real solution for u and  only if the focal length f is
greater than one-fourth of the distance between the object and image.
(41) When a number of thin lenses are placed in contact,
(a) power of the equivalent lens is equal to sum of the powers of the individual lenses i.e.
P = P1 + P2 + P3 + … ,
(b) magnification produced is equal to the product of the magnifications produces by the
component lens i.e.
m = m1  m2  m3  …
(42) Consider that an object is placed at a distance u from a convex lens of focal length f and
its image is formed at a distance  from the lens. If the object starts moving towards (or
away) from the lens, then
du
(rate of change of position of the object i.e. its speed) and
dt
d
(speed of the image) are related to each other by the reflection
dt
f2
du
d

=
2
dt
u  f  dt
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(43) Consider that an equiconvex lens (each surface having radius of curvature R) of
focal length f. Its focal length is given by
1

f
1
1
   1  R  R 


2    1

R
(a) When the lens is cut along XOX’ as shown in figure, the
Y
radii of curvature of the two surfaces of the lens remain
unchanged. Hence, the focal length of a half portion of
the lens still remains equal to f.
X’
o
(b) When the lens is cut along YOY’ as shown in figure, a
half portion of the lens becomes a plano-convex lens the
focal length of half portion of the lens, when cut along YOY’
is given by
1

f'
1
1
   1  R   



   1
R
It follows that f’ = 2f.
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Y’
X
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(44) (a) Consider that the plane surface of a plano-convex of focal length f and the curved
surface of radius of curvature R is silvered as shown in figure (1)
(1)
(2)
When light from an object falls on its curved surface, first of all its image is formed due
to refraction by the lens, then due reflection by the silvered plane surface and finally
again due to refraction (the rays reflected from the silvered surface are again
refracted) by the lens.
If F is the equivalent focal length of the system (lens, plane mirror and lens), then
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1
1 1 1
1 1 1
2




 

F
f fm f
f  f
f

fm   
or F = f/2
(b) Consider that one surface of an equiconvex of focal length f and curved surface of
radius of curvature R is silvered as shown in figure (2).
When light from an object falls on its unsilvered surface, first of all its image is formed
due to refraction by the lens, then due to reflection by the silvered surface acting as a
concave mirror and finally again due to refraction (the rays reflected from the silvered
surface are again refracted) by the lens.
If F is the equivalent focal length of the system (lens, concave mirror and lens), then
1
1 1 1
1
1
1
1 1 
R  f 






 2    2

F
f fm f
f R /2 f
f R
 fR 
or F =
fR
2(R  f)
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
fm  R / 2
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(45) There are two values of the angle of incidence, for which a ray passing through a prism
deviates through a given angle.
(46) A prism always deviates a ray of light towards its base. When a prism, made of material
of refractive index// is placed in a medium of refractive index ’ (’<), the prism still
deviates the light towards its base. But the angle of deviation decreases.
(47) When a prism, made of material of refractive index  is placed in a medium of refractive
index ’ (’ >), the prism still deviates the light towards away from the base.
(48) The white light gets dispersed, while passing through a prism due to the fact that white
light consists of light of different wavelengths. Since the refractive index of the material of
a prism depends upon the wave length of light, the light of different wavelengths undergo
unequal deviations, while passing through the prism.
(49) When white light passes through a glass slab having parallel faces, it is dispersed into its
constituent colours also, as it undergoes refraction at the first face. However, the
constituent colours recombine to produce white light, when refraction takes place at the
second face of the glass slab.
o
(50) The Fraunhoffer lines F, D and C in the solar spectrum possess wavelengths 4,861 A ,
o
o
5,890 A and 6,563 A respectively and lie in blue, yellow and red regions of the spectrum.
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Sometimes, refractive indices of the materials of prisms for blue, mean and red light i.e.
b,  and r are represented by F, D and C respectively.
(51) When two prisms (of different materials and angles of prism) are combined so as to
produce dispersion without deviation, the condition for no deviation applies to the path of
mean light.
(52) When two prisms, one of crown glass and the other of flint glass, are combined to produce
dispersion without deviation, the order of the colours in the spectrum due to the
combination is opposite to that due to the crown glass prism.
(53) The chromatic aberration in a lens is because of the fact that it has different focal lengths
for light of different colours.
(54) The pure spectrum can be obtained by placing the prism in minimum deviation position.
(55) When light from the sun traverses the atmosphere, the scattering of the blue light is
approximately sixteen times as large as that of red light.
(56) The formation of rainbows is due the phenomena of dispersion and total internal reflection
of white light (from the sun) from the water droplets suspended in the air.
(a) In the formation of primary rainbow, a single total internal reflection takes place;
while the secondary rainbow is the result of double total internal reflection.
(b) In the primary rainbow, the upper edge is red; while in the case of the secondary
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rainbow, the upper edge is violet.
(c) The primary rainbow is much brighter than the secondary rainbow.
(57) The maximum value of the angle of prism is equal to twice the critical angle.
(58) The dispersive power of the material of the prism is independent of the shape (angle of
prism) or size of the prism. It depends only on the refractive index of the material of the
prism.
(59) Consider two prisms one of crown glass and the other of flint glass having angles of prism
A and A' respectively be the angles of the crown glass and flint glass prisms respectively.
For crown glass, let ,  and r be the refractive indices for violet, mean and red lights
and , its dispersive power. Similarly, for the flint glass, the corresponding values be v',
’, r’ and ’ be the corresponding values for the flint glass. The values of refractive index
and dispersive power for flint glass are greater than those for crown glass. Thus, ’ >
 and ’>.
(a) Dispersion without deviation :
(i) Condition for dispersion without deviation,
A'
 1
 
A
 ' 1
Since ’ > , it follows that A > A'. It implies that to produce dispersion without
deviation, the angle of crown glass prism has to be greater than that of flint glass
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prism.
(ii) Net angular dispersion =  ( - ’)
Since ’ >  the factor  - ’ and hence
 { - ’} is negative. It implies that
the order of the colours in the spectrum due to combination is opposite to that
due to crown glass prism alone.
(b) Deviation without dispersion :
(i) Condition for deviation without dispersion,

'
 
'

It implies that/or no dispersion, the materials and the angles of the two prisms
should be chosen, so that their dispersive powers are in inverse ratio of the
deviations suffered by mean light through them.
Also as ’ > , it follows that  > ’ i.e. A(-1) > A' ('-1)
Since ' - 1 >  - 1, it follows that A > A'. It implies that to produce deviation
without dispersion, the angle of crown glass prism has to he greater than that of
the flint glass prism.


(ii) Net deviation =  1  
' 

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Since ’>, 1-

will be positive. It implies that the combination will
'
produce deviation in the same direction as produced by the crown glass
prism.
(60) According to Rayleigh's scattering law, when the light traverses the atmosphere, the
intensity of light scattered is inversely proportional to the fourth power of the wavelength
of the light. As a consequence of it:
(a) The danger signals are red in colour. It is because, due to its large wavelength, the
scattering of red light is only to a small extent. Accordingly, the red light signals can
be seen upto a longer distance without much loss in their intensity.
(b) The colour of sky looks blue. It is because, due to its small wavelength, the scattering
of blue light is prominent and the sky looks blue.
(c) The colour of sky on the moon appears white. It is because, moon has no
atmosphere.
(61) The optical instruments are used as an aid to the human eye so as to produce higher
magnification, greater resolving power and to produce the image of close lying objects at
the least distance of distinct vision.
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(62) Eye is a natural optical instrument. It has a unique feature of automatic adjustment of its
aperture and focussing.
(63) A pigment, contained in the iris, determines the colour of the eye.
(64) The optic nerve conveys the light signals from the retina to the brain, which are then
interpreted as the image of an object, cussing.
(65) Whereas the rods distinguish light from dark in low light intensities; the cones distinguish
frequency ranges of sufficiently intense light, which the brain interprets as light of
different colours.
(66) The farsightedness occuring with age is called presbyopia.
(67) Astigmatism is caused due to the non-spherical shape of the cornea or the crystalline
lens. It is cured by using non-spherical lenses.
(68) A simple microscope is a convex lens of short focal length.
(69) The magnifying power and magnification produced by a lens are different from each other.
(70) In case of a simple microscope, the maximum magnification occurs, when the image is
formed at the near point (at least distance of distinct vision) of the eye. For relaxed eye
viewing (when the image is formed at infinity), the magnification is 1 less.
(71) In a compound microscope, object lens is of short focal length and short operature, while
eye lens has short focal length and large aperature.
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(72) In a telescope, object lens is of large focal length and large operature, while eye lens has
short focal length and short aperature.
(73) In a telescope, the distance between object lens and eye lens depends upon the position
of the object. The telescope is focussed on a distant object by varying the distance
between the two lenses with the help of rack and pinion arrangement.
(74) The increase in aperture of the objective of a telescope increases the brightness of the
image.
(75) The increase in aperture of the objective of a telescope increases its resolving power. The
resolving power also increases, when light of shorter wavelength are used to see the
distant object.
(76) The image in a prism binocular is free from lateral inversion.
(77) The range of the object distances, over which the objects are in reasonably good focus is
called the depth of focus.
(78) In a camera, the lens has a constant focal length and the image distance is varied by
moving the lens to produce a sharp image of the object on the film for different object
distances. In the eye, the image distance is constant and the focal length of the
lens is varied to produce a sharp image of the object on the retina.
(79) A person suffering from nearsightedness (or myopia) is unable to see the far off objects
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clearly. This defect of vision is cured by using spectacles (or contact lenses) consisting of
concave lenses.
(80) A person suffering from farsightedness (or hypermetropia) is unable to see the nearby
objects clearly. This defect of vision is cured by using spectacles (or contact lenses)
consisting of convex lenses.
(81) When a telescope is in normal adjustment, the distance between the objective and eyepiece is equal to the length of the telescope tube.
(82) In a telescope, the image is actually not magnified. It simply increases the visual angle of
the object. The magnifying power of a telescope is perceived as the increase in the visual
angle of the image.
(83) In a camera, the normal exposure times are
1
1
1
1
1
s,
s,
s,
s,
s ……. etc
500 250 125 60 30
(84) Aperture of the camera refers to the diameter (d) of the circular opening through which
the light enters the camera and falls on the film. This is normally expressed as a fraction
of the focal length (f) of the camera lens and are usually called as the f-numbers.
Normally, following apertures are used in a camera :
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f f
f
f
f f
f
….etc
,
, ,
, ,
,
2 2.8 4 5.6 8 11 16
Corresponding to the apertures of the sizes given above, the areas of the different
apertures will be in the ratio
1:1/2:1/4:1/8:1/16:1/32:1/64 …
(roughly)
(85) The wave front is always perpendicular to the direction of rays of light.
(86) The time taken for light to travel from one wave front to another is the same along any
ray.
(87) The phase difference between any two points on a wavefront is zero.
(88) When a wave undergoes reflection from a denser medium, a phase change of it takes
place.
(88) When a wave undergoes refraction, no change in phase takes place.
(89) As a wave front progresses, the amplitude of a
(a) Plane wave front remains constant,
(b) Spherical wave front varies inversely as the distance(i.e. as 1/r) from the source of
Light and
(c) Cylindrical wave front varies inversely as the square root of the distance (i.e. as 1/ r )
from the source of light.
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(90) The intensity of light is determined by the square of amplitude of wave.
(91) The contribution of a wavelet in any direction making angle  with the normal to the
wavelet is proportional to
1
2
(1 + cos 0). Since for a wavelet, which lies oh the back of
the secondary wave front,  is 180°, the contribution from such a wavelet is
1
(1 + cos
2
180°) = 0.
(92) The intensity of light is directly proportional to the square of the amplitude of the wave.
(93) In the interference pattern produced by two narrow slits, the intensity of all the bright
fringes is same.
(94) The fringes obtained in Young's double slit experiment are hyperbolic in shape. In a small
interference pattern or when D » d, the fringes appear straight.
(95) The law of conservation of energy is obeyed in the phenomenon of interference of light.
The light energy which disappears at the regions of destructive interference appears at
the regions of constructive interference so that the average intensity of light remains the
same.
(96) The colour of thin films is due to the interference between the two beams of light; one
reflected from the upper surface of the film and the other emerging after reflection from
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the lower surface of the film.
(97) In the interference pattern produced by two narrow slits, the fringe width decreases
(i) on using light of smaller wavelength (as   ),
(ii) on decreasing distance between slits and the screen (as   D),
(iii) on increasing distance between the two slits (as   1/d ) and
(iv) on replacing the medium between the slits and the screen by a medium of higher
refractive index (as the wavelength of light used reduces to  /  ).
(98) When two light waves of amplitudes a1 and a2 differing in phase by  interfere, the
intensity of the resultant light is given by
I = a12 + a22 + 2a1 a2 cos 
(i) The intensity of light will be maximum, when  = 0.
Imax = a12 + a22 + 2 a1 a2 cos 0 = a12 + a22 + 2a1 a2  1 = (a1 + a2)2
(ii) The intensity of light will be minimum, when  = .
Imin = a12 + a22 + 2 a1 a2 cos  = a12 + a22 + 2 a1 a2 x (-1) = (a1 - a2)2
(99) If in an interference experiment, nth bright fringe due to wavelength X coincides with the
nth bright fringe due to wavelength ', then
nD  n'D  '

or n = n’'
d
d
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(100) In the Young's double slit experiment, if a thin glass sheet of thickness t is introduced in
the path of light from one of the two slits, the central bright fringe displaces in the
direction of that slit. If y is the distance through which the central bright fringe moves,
then
yd
 (  1) t
D
(101) The diffraction of light is observed, when size of the obstacle is of the order of wavelength
of light.
(102) Interference is the result of superposition of light waves from two sources, whereas
diffraction takes place due to interference of light waves from the different parts of the
same source of light.
(103) All the secondary maxima are not of the same intensity. The intensity of secondary
maxima goes on decreasing with the order of the maximum.
(104) The intensity of central maximum is independent of the slit width. However, the slit width
affects the width of the central maximum. The wider the slit is, the narrower is the
central diffraction maximum.
(105) The phenomenon of diffraction limits the resolving power of an optical instrument.
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(106) In the diffraction pattern produced by a narrow slit, the width of the central maximum
decreases
(i) on using light of smaller wavelength (as 0  ).
(ii) on decreasing distance between slits and the screen (as 0  D) and
(iii) on increasing distance between the two slits (as 0  1/a ).
(107) In diffraction pattern produced by a single slit, all secondary maxima and minima are of
same width and the central maximum is twice as wide as any other secondary maximum
or minimum.
(108) Two objects are said to be just resolved, if the separation between the central maxima of
their diffraction patterns is just equal to distance between the central maximum and first
secondary minimum of any of the two objects.
(109) When viewed by the eye of pupil diameter D, two points located at a distance y from it
will be just resolved, if the minimum distance d between the two points is given by
d
1.22
yD
where  is the wavelength of light used.
(110) The phenomenon of polarisation establishes that light is transverse in nature.
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(111) The naked eye cannot distinguish between the ordinary light and the plane polarised
light.
(112) The ordinary light from a source of light is unpolarised.
(113) The vibrations in plane polarised light are perpendicular to the plane of polarisation.
(114) In a plane polarised light, the variations in electric field vector are confined to a plane
perpendicular to the direction of propagation of light.
(115) When a polariser is rotated in the path of ordinary light, the intensity of light remains
undiminished. The intensity of light transmitted from the polariser changes, in case the
light falling on the polariser is plane polarised light. As such, the polariser is said to be
acting as an analyser.
(116) When (N+1) polaroids are placed, so that their axes are equally spaced, then the
intensity of light after passing through all the polaroids is given by
2N
 

I  I0  cos
2N 

where Io is intensity of the incident light.
(117) In Young's double slit experiment, the width of all the fringes (bright, dark and central)
is same.
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{Std 12th Physics CBSE_CH. 10 – Wave Optics – Experts tips}