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A small candle 2.5 cm in size is placed 27 cmin front of a concave mirror of radius ofcurvature 36 cm. At what distance from themirror should a screen be placed in order toreceive a sharp image? Describe the natureand size of the image. If the candle is movedcloser to the mirror, how would the screen haveto be moved?
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A cm needle is placed 12 cm away from a
convex mirror of focal length 15 cm. Give thelocation of
the image and magnification.
Describe what happens as the needle is movedfarther from
the mirror.
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A tank is filled with water to a height of 12'5
cm. The apparent depth of the needle lying atthe bottom of the tank is measured by amicroscope to be 9-4 cm. What is the refractive index of water? If water is replaced by a liquidof refractive index 6.3 upto the same height,by what distance would the microscope have tobe moved to focus on the needle again ?
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The following
figures (a) and (b) showrefraction of an incident ray in air at 60° withthe
normal to glass-air and water-air interface,respectively. Predict the angle of
refraction ofan incident ray in water at 45° with the normalto a water-glass
interface
(a) (b)
(c)
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A small bulb is placed at the bottom of a tank
containing water to a depth of 80 cm. What isthe area of the surface of water through whichlight from the bulb can emerge out ? Refractive index of water is 1.33 (consider the bulb to be apoint source).
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A prism is made of glass of unknown refractiveindex. A parallel beam of light is incident on aface of the prism. By rotating the prism, theangle of minimum deviation is measured to be40°. What is the refractive index of thematerial of the prism ? If the prism is placed in water (refractive index 1.33), predict the newangle of minimum deviation of a parallel beam of light. The refracting angle of the prism is60°.
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Double-convex lenses are to be manufacturedfrom a glass of refractive index 1'55, with bothfaces of the same radius of curvature. What isthe radius of curvature required if the focallength is to be 20 cm ?
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A beam of light,converges to a point P. A lensis placed in the path of the convergent beam 12 cm from P. At what point does the beamconverge if the lens is (a) a convex lens of focallength 20 cm, (b) a concave lens of focal length16cm ?
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An object of size 3'0 cm is placed 14 cm infront of a concave lens of focal length 21 cm.
Describe the image produced by the lens. Whathappens if the object is moved farther from thelens ?
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What is the focal length of a convex lens of focallength 30 cm in contact with a concave lens offocal length 20 cm ? Is the system a converging ora diverging lens ? Ignore thickness of the lenses.
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A compound microscope consists of an objective lens of focal length 200 cm and an eye-piece of focal length 6025 cm separated by a distance of15 cm. How far from the objective should anobject be placed in order to obtain the final imageat (a) the least distance of distinct vision (25cm), (b)infinity ? What is the magnifying powerof the microscope in each case ?
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A small telescope has an objective lens of focallength 144 cm and an eye-piece of focal length 6.0 cm. What is the magnifying power of the telescope? What is the separation between the objective and eye-piece?
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(a) A giant
refracting telescope at an observatoryhas an objective lens of focal length
15m. If aneye-piece of focal length 1.0 cm is used, what isthe angular
magnification of the telescope ?
(b) If this
telescope is used to view the moon,
what is the diameter
of the image of the moonformed by the objective lens ? The diameterof the moon
is
and
the radius of lunar orbit is
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Use the mirror equation to deduce that
(a) an object placed between f and 2f ofa concavemirror produces a real image beyond 2f.
(b)a convex mirror always produces a virtualimage independent of the location of the object.
(c) the virtual image produced by a convex mirror is always diminished in size and islocated between the focus and the pole.
(d)an object placed between the pole and focusof a concave mirror produces a virtual andenlarged image.
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A small pin fixed on the table top is viewedfrom above from a distance of 50 cm. By whatdistance would the pin appear to be raised if itis viewed from the same point through a 15 cmthick glass slab held parallel to the table ?
Refractive index of glass = 1.5. Does the answerdepend upon the location of the slab?
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(a) Following figure
shows a cross-section of a 'light pipe? made of glass fibre of refractive index
1.68. The outer covering of the pipe ismade of material of refractive index 1.44.
Whatis the range of the angles of incident rays withthe axes of the pipe for
which the total internalreflection inside the pipe take place as shownin the
figure ?
(b) What is
the answer if there is no outercovering of pipe ?
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Answer the following questions ;
(a) You have learned that plane and convexmirrors produce virtual images of objects. Canthey produce real images under somecircumstances ? Explain.
(a)A virtual image, we always say, cannot be
caught on a screen. Yet when we 'see' a virtualimage, we are obviously bringing it on to the 'screen' (i.e., the retina) of our eye. Is there acontradiction ?
(c) A diver under water, looks obliquely at afisherman standing on the bank of a lake, wouldthe fisherman look taller or shorter to thediver than what he actually is ?
(d) Does the apparent depth of a tank of waterchange if viewed obliquely ? If so, does theapparent depth increase or decrease ?
(e) The refractive index of diamond is much greater than that of ordinary glass. Is this factof some use to a diamond cutter ?
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The image of a small electric bulb fixed on thewall of a room is to be obtained on the oppositewall 3 m away by means of a large convex lens.
What is the maximum possible focal length ofthe lens required for the purpose ?
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A screen is placed 90 cm from an object. Theimage of the object on the screen is formed byconvex lens at two different locationsseparated by 20 cm. Determine the focal lengthof the lens.
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(a) Determine the effective focal length of thecombination of the two lenses in the question
9.10 if they are placed 8.0 cm apart with theirprincipal axes coincident. Does the answerdepend on which side a beam of parallel light isincident ? Is the notion of effective focal lengthof this system useful at all ?
(b) An object 1.5 cm in size is placed on theside of the convex lens in the abovearrangements. The distance between the objectand the convex lens is 40 cm. Determine themagnification produced by the two-lens system,and the size of the image.
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At what angle should a ray of light be incidenton the face of a prism of refracting angle 60°so that it just suffers total internal reflectionat the other face? The refractive index of the material of the prism is 1.524.
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You are given prism made of crown glassand flint glass with a wide variety of angles.
Suggest a combination of prisms which will
(a) deviate a pencil of white light withoutmuch dispersion (6) disperse (and displace) apencil of white light without much deviation
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for a normal eye, the far point is at infinityand the near point of distinct vision is about 2.5 cm in front of the eye. The cornea of the eyeprovides a converging power of about 40dioptres, and the least converging power of theeye lens behind the cornea is about 20 dioptres.
From this rough data estimate the range ofaccommodation (i.e., the range of converging
power of the eye-lens) of a normal eye.
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Does short-sightedness (myopia) or long.sightedness (hypermetropia) imply necessarilythat the eye has partially lost its ability ofaccommodation ? If not, what might cause thesedefects of vision ?
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A myopic person has been using spectacles of power- 1.0 dioptres for distant vision. Duringold age he also needs to use separate readingglass of power +2 dioptres. Explain what may have happened.
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A person looking at a mesh of crossed wires isable to see the vertical wires more distinctly thanthe horizontal wires. What is this defect due to ?
How is such a defect of vision corrected ?
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A man with normal near point (25 cm) reads abook with small print using a magnifying glass: a thin convex lens of focal length 5 cm.
(a) What is the closest and the farthestdistance at which he can read the book when
viewing through the magnifying glass ?
(b) What is the maximum and minimumangular magnification (magnifying power)possible using the above simple microscope ?
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A card sheet divided into squares each of size1 mm2 is being viewed at a distance of 9 cmthrough a magnifying glass (a converging lensof focal length 10 cm) held close to eye.
(a) What is the magnification (image size/objectsize) produced by the lens ? How much is thearea of each square in the virtual object ?
(b) What is the angular magnification(magnifying powers) of the lens ?
(c) Is the magnification in (a) equal tomagnifying power in (b) ? Explain.
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(a) At what distance should the lens be heldfrom the figure in the above exercise in order
to view the squares distinctly with maximum
possible magnifying power ?
(b) What is the magnification (image size/object size) in this case ?
(c) Is the magnification equal to magnifyingpower in this case ? Explain.
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What should be the distance between the objectin the previous exercise and the magnifyingglass if the virtual image of each square in thefigure is to have an area 6'25 mm2 ? Wouldyou be able to see the squares distinctly withyour eyes very close to the magnifier ?
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An angular magnification (magnifying power)
of 30 X is desired using an objective of focal length 1.25 cm and eye piece of focal length cm. How will you set up the compoundmicroscope ?
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A small telescope has an objective lens of focallength 140 cm and an eye piece of focal length5'0 cm. What is the magnifying power of thetelescope for viewing distant objects when
(a) the telescope is in normal adjustment (i.e.,when the final image is formed at infinity) ?
(b)the final image is formed at the leastdistance of distinct vision (25 cm) ?
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For the telescope described in the last exercise,in 9.34
(a), what is the separation between theobjective lens and the eye-piece?
(b) If this telescope is used to view a 100 m talltower 3 km away, what is the height of image ofthe tower formed by objective lens?
(c) What is the height of final image of thetower if it is formed at 25cm ?
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A cassegrain
telescope uses two mirrors asShown in figure. Such a telescope is built
withmirrors 20 mm apart. If the radius of curvatureof large mirror is 220 mm
and the small mirroris 140 mm, where will be the final image of anobject at infinity
be?
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The adjoining figure
shows an equiconvex lens (of refractive index 1.50) in contact with a
liquidlayer on top of a plane mirror. A small needle
with its tip
on the principle axis is moved alongthe axis until its inverted image is found
at theposition of the needle. The distance of the needlefrom the lens is
measured to be 45*0 cm. Theliquid is removed and the experiment is repeated.
The new
distance is measured to be 30.0 cm.
What is the
refractive index of liquid ?
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question_answer36)
A ray of light
incident at an angle 9 on a refracting face of a prism emerges from the other
face normally. If the angle of the prism is 5° and the prism is made of a
material of refractive index 1-5, the angle of incidence is
(a)
7.5° (b)5°
(c)
15° (d) 2-5°
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question_answer37)
A short pulse of
white light is incident from air to a glass slab at normal incidence. After travelling
through the slab, the first colour to emerge is
(a)
blue (b) green
(c)
violet (d) red
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question_answer38)
An object
approaches a convergent lens from the left of the lens with a uniform speed 5
m/s and stops at the focus. The image
(a) moves away from the lens with uniform speed 5 m/s
(b) moves
away from the lens with uniform acceleration
(c)
moves away from the lens with a non-uniform acceleration
(d)
moves towards the lens with a non-uniform acceleration
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question_answer39)
A passenger in an
aeroplane shall
(a) never see a rainbow
(b) may see a primary and a secondary rainbow as concentric
circles
(c) may see
a primary and a secondary rainbow as concentric arcs
(d)
shall never see a secondary rainbow
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question_answer40)
You are given four
sources of light each one providing a light of a single colour - red, blue, green
and yellow. Suppose the angle of refraction for a beam of yellow light
corresponding to a particular angle of incidence at the interface of two media
is 90°. Which of the. following statements is correct if the source of yellow light
is replaced with that of other lights without changing the anlge of incidence ?
(a) The beam of red light would undergo total
internal
reflection
(b)
The beam of red light would bend towards normal while it gets refracted through
the second medium
(c)
The beam of blue light would undergo total internal reflection
(d)
The beam of green light would bend away from the normal as it gets refracted
through the second medium
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question_answer41)
The radius of
curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive
index of the material of the lens be 1-5, it will
(a) act as a convex lens only for the objects that lie on
its curved side
(b) act as
a concave lens for the objects that lie on its curved side
(c)
act as a convex lens irrespective of the side on which the object lies
(d)
act as a concave lens irrespective of side on which the object lies
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question_answer42)
The phenomena involved
in the reflection of radiowaves by ionosphere is similar to
(a)
reflection of light by a plane mirror
(b)
total internal reflection of light in air during a mirage
(c)
dispersion of light by water molecules during the formation of a rainbow
(d)
scattering of light by the particles of air
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question_answer43)
The direction of
ray of light incident on a concave mirror is shown by PQ while directions in
which the ray would travel after reflection is shown by four rays marked 1,2, 3
and 4, Fig. 6(EP).l Which of the four rays correctly shows the direction of
reflected ray?
(a)
1 (b) 2
(03
(d)4
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question_answer44)
The optical density
of turpentine is higher than that of water, while its mass density is lower.
Fig. 6(EP).2 shows a layer of turpentine floating over water in a container.
For which one of the four rays incident on turpentine in Fig. 6(EP).2, the path
shown is correct ?
(a)
1 (b) 2
(c)
3 (d) 4
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question_answer45)
A car is moving
with a constant speed of 60 km h-1 on a straight road. Looking at
the rear view mirror, the driver finds that car following him is at a distance
of 100 m and is approaching with a speed of 5 km h-1 . In order to
keep track of the car in the rear, the driver begins to glance alternatively at
the rear and side mirror of his car after every 2 s till the other car
overtakes. If the two cars were maintaining their speeds, which of the following
statement (s) is/are correct ?
(a)The speed of the car in the rear is 65 km h-1
(b) In the side mirror, the car in the rear would appear to
approach with a speed of 5 km h-1 to the driver of the leading car
(c) In the
rear view mirror, the speed of the approaching car would appear to
decrease as the distance between the cars decreases
(d)
In the side mirror, the speed of the approaching car would appear to increase
as the distance between the cars decreases
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question_answer46)
There are certain
materials developed in laboratories which have a negative refractive index,
Fig. 6(EP).3. A ray incident from air (medium 1) into such a medium
(medium 2) shall follow a path given by
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question_answer47)
Consider an
extended object immersed in water contained in a plane through. When seen from
close to the edge of the trough, the object looks distorted because
(a) the apparent depth of the points close to the edge are
nearer the surface of the water compared to the points away from the edge.
(b) the
angle subtended by the image of the object at the eye is smaller than the
actual angle subtended by the object in air.
(c)
some of the points of the object far away from the edge may not be visible
because of total internal reflection.
(d)
water in a trough acts as a lens and magnifies the object.
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question_answer48)
A rectangular block
of glass ABCD has a refractive index 1.6. A pin is placed midway on the face
AB, Fig. 6(EP).4. When observed from the face AD, the pin shall
(a) appear to be near A.
(b) appear to be near D.
(c) appear to be at the centre of AD.
(d) not be seen at all.
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question_answer49)
Between the primary
and secondary rainbows, there is a dark band known as Alexandra?s dark band.
This is because
(a) light scattered into this region interferes destructively.
(b) there
is no light scattered into this region.
(c)
light is absorbed in this region.
(d)
angle made at the eye by the scattered rays with respect to the incident light
of the sun lies between approximately 42° and 50°.
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question_answer50)
A magnifying glass
is used, as the object to be viewed can be brought closer to the eye than the
normal near point. This results in
(a) a larger angle to be subtended by the object at the eye
and hence viewed in greater detail.
(b) the
formation of a virtual erect image.
(c)
increase in the field of view.
(d) infinite magnification at the near point.
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question_answer51)
An astronomical
refractive telescope has an objective of focal length 20 m and an eyepiece of focal
length 2 cm.
(a) The length of the telescope tube is 20-02 m.
(b) The magnification is 1000.
(c) The image formed is inverted.
(d) An objective of a larger aperture will increase the
brightness and reduce chromatic aberration of the image.
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question_answer52)
Wil the focal
length of a lens for red light be more, same or less than that for blue light ?
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question_answer53)
The near vision of
an average person is 25 cm. To view an object with an angular magnification of
10, what should be the power of the microscope ?
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question_answer54)
An unsymmetrical
double convex thin lens forms the image of a point object on its axis. Will the
position of the image change if the lens is reversed ?
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question_answer55)
Three immiscible liquids
of densities d1> d2> d3 and refractive
indices ( are put in a beaker. The height
of each liquid column is A dot is made
at the bottom of the beaker. For near normal vision, find the apparent depth of
the dot.
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question_answer56)
For a glass prism , the angle of minimum deviation
is equal to the angle of the prism.
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question_answer57)
A short object of
length L is placed along the principal axis of a concave mirror away from
focus. The object distance is u. If the mirror has a focal length, what will be
the length of the image? You ma; take .
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question_answer58)
A circular disc of
radius *R' is placed co-axially and horizontally inside an opaque hemispherical
bowl of radius 'a', Fig. 6(EP).9. The far edge of the disc is just visible when
viewed from the edge of the bowl. The bowl is filled with transparent liquid of
refractive index p. and the near edge of the disc becomes just visible. How far
below the top of the bowl is the disc placed ?
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question_answer59)
A thin convex lens of
focal length 25 cm is cut into two pieces cm
above the principal axis. The part is placed at (0, 0) and an object placed at
(- 50 cm, 0). Find the coordinates of the image.
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question_answer60)
In many experimental
set-ups the source and screen are fixed at a distance say D and the lens is movable.
Show that there are two positions for the lens for which an image is formed on
the screen. Find the distance between these points and the ratio of the image
sizes for these two points.
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question_answer61)
A jar of height h
is filled with a transparent liquid of refractive index |i, Fig. 6(EP).12. At
the centre of the jar on the bottom surface is a dot Find the minimum diameter
of a disc, such that when placed on the top surface symmetrically about the
centre, the dot is invisible.
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question_answer62)
A myopic adult has
a far point at 0-1 m. His power of accomodation is 4 diopters, (i) What power lenses
are required to see distant objects? (ii) What is his near point without glasses?
(iii) What is his near point with glasses? (Take the image distance from the
lens of the eye to the retina to be 2 cm.)
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question_answer63)
Show that for a material
with refractive index , light incident at any
angle shall be guided along a length perpendicular to the incident face.
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question_answer64)
The mixture of a
pure liquid and a solution in a long vertical column (i.e., horizontal
dimensions « vertical dimensions) produces diffusion of solute particles and
hence a refractive index gradient along the vertical dimension. A ray of light
entering the column at right angles to the vertical is deviated from its
original path. Find the deviation in travelling a horizontal distance d « h,
the height of the column.
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question_answer65)
If light passes
near a massive object, the gravitational interaction causes a bending of the
ray. This can be thought of as happening due to a change in the effective
refractive index of the medium given by
where r
is the distance of the point of consideration from the centre of the mass of
the massive body, G is the universal gravitational constant, M the mass of the
body and c the speed of light in vacuum. Considering a spherical object, find
the deviation of the ray from the original path as it grazes the object
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question_answer66)
An Infinitely long
cylinder of radius R is made of an unusual exotic material with refractive
index (-1), Fig. 6(EP). 17. The cylinder is placed between two planes whose
normals are along the y directions. The center of the cylinder O lies along the
y-axis. A narrow laser beam is directed along the y direction from the lower
plate. The laser source is at a horizontal distance x from the diameter in the
y direction. Find the range of x such light emitted from the lower plane does
not reach the upper plane.
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question_answer67)
(i) Consider a
thin lens placed between a source (s) and an observer (), Fig. 6(EP).18. Let the thickness
of the lens vary as w (b) ,where b is the
vertical distance from the pole. is a " constant
Using Format's principle, i.e., the time of transit for a ray between the
source and observer is an extremum, find the condition that all paraxial rays
starting from the source will converge at a point on
the axis. Find the focal length.
(ii) A
gravitational lens may be assumed to have a varying width of the form
Show that
an observe will see an image of a point object as a ring about the center of
the lens with an angular radius
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