PHYSICS 08-11-11 Assgnament With Solutions

8/13/2019 PHYSICS 08-11-11 Assgnament With Solutions

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NARAYANA EDUCATONAL INSTITUTIONSVIJ-I-ZONE.

IIT - PHYSICS ASSIGNMENT (DT.08-11-11)TOPICS : RAY OPTICS, PHYSICAL OPTICS, ROTATIONAL MOTION

==========================================================================01. A plane mirror is placed with its plane at an angle of 30 0 with the y-axis.

Plane of the mirror is perpendicular to the xy plane and the length of themirror is 3m. as insect moves along x-axis starting from a distant pointwith a speed 2cm/s. the duration of the time for which the insect can seeits own image in the mirror isa 300s ! 200s c 1"0s d 100s

#ol$ A#%&. 'n the figure shown the line (%A) is normal to the mirror passing through the end

point A. *y ray diagram it can !e shown that when the insect is to the left of (%)

all its reflected rays will !e towards right of (%). #o it cannot see its image !ecause says are not reaching it. +hen the insect is the right of (%) its reflectedrays will !e on !oth sides of the insect. ,hat means the insect is in the field ofview of its image. #o it can see its image. #o it can see the image till it reachesthe point (*) of the mirror from point (%).

0

32 100

cos-0

= t

%r t 300 seconds.

02. atch the following

Column I Column II

A iverging lens p ocal length does not change on

dipping in water * onverging lens 4 Always forms a virtual5 erect and

diminished image of a real o!6ectoncave mirror r an form virtual5 erect and

magnified image of a real o!6ectonvex mirror s an form real5 inverted and

diminished image of a real o!6ectt ocal length changes on dipping

in water.

#ol$ onceptual

03. A particle is dropped along the axis from a heightf 2

on a concave mirror of

focal (f) length f as shown in the figure. ,he acceleration due to gravity is g.ind the maximum speed of image.

a gf ! 3 3fg7

c 2gf d 1 2gf 7

#ol$ *#%&. 'f the distance of the virtual image from the pole is y 8 x is o!6ect distance5 then


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( )

2

2

'

'

'' max

1 1 1 fxy

y x f f x

dy f dx 9ow5

dt f x dt

f f v 2g x

f x 2

for v to !e maximum

dv f 30 x v 3fg

dx 3 7

= =

=

=

= = =

07. A !eam of diameter d is incident on a glass hemisphere as shown in figure. 'f the radius ofcurvature of the hemisphere is very large in comparision to d5 then diameter of the !eam at the

!ase of the hemisphere will !e

A 3d/7 * d d/3 2d/3#ol$

#%&. :efraction at the curved surface 2 1 2 1v u : =

1PP is very small

1

1

AP *P

=1 1AP d5 P v= =

Paragraph for Question Nos.05 to 07 PASSAGE 3

igure A shows two thin lenses & 1 and & 2 placed in contact with a common optical axis. ,helenses5 !ecause their nature is not specified are shown as dotted lines. ,hese lenses are made ofthe same material. An o!6ect of si;e 2 cm is


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#ol$ *

#%&. >iven magnification3 v

m2 u

= = 5 here u ?1 cm. ocal length of the com!ination is 1 1 1f v u

=

0 . istance !etween the o!6ect and the screen isA 1 0 cm * 120 cm 100 cm =0 cm

#ol$

#%&. >iven for second casev 3

u 2= 5 also v u 20 = . istance !etween the screen and lens D v u= + .

%n solving we get v 0 cm and u 70 cm.

0@. +hich of the following is correctA &2 is convex lens of focal length 27 cm * & 2 is concave lens of focal length 27 cm

&2 is concave lens of focal length 7= cm & 2 is convex lens of focal length 7= cm#ol$

#%&. ocal length of the & 1 is1

1 1 1f 60 40

= . ocal length of the com!ination is 7= cm. ocal length of

the lens & 2 is1 2

1 1 1f f f

= +

0=. &ight waves travel in vaccume along the y-axis. +hich of the following may represent thewavefrontA x constant * y constant ; constant x y ;+ + constant

#ol$ *Belocity of light is always perpendicular to the wavefront.

0C. Statement 1: ,win


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11. A prism placed in air made up of flint glass is such that the any incident ray on one surface doesnot emerge from the second surface. ritical angle for flint glass is 3 0 in air. ,hen5 refractingangle A may !ea 3@0 ! "7 0 c @10 d @30

#ol$#%&. or ray to not emerge from second surface5 r 2 E

2minr

1maxA r

5*ut 1maxr = when i C0 0

A 2 0A @2

12. STATE"ENT-1 : A ray is incident from outside on a glass sphere surrounded !y air as shown.,his ray may suffer total internal reflection at second interface.

Fi !"i#"$ f%&$

S$&'#i#"$ f%&$

i#&i $#"%

*+%!!!,-$ $ %i

STATE"ENT-2 : or a ray going from denser to rarer medium5 the ray may suffer totalinternal reflection.

#ol$#%&. rom symmetry the ray shall not suffer ,': at second interface5 !ecause the angle of incidence at

first interface e4uals to angle of emergence at second interface. Fence statement 1 is false.

13. &ight from source falls on lens and screen is placed on the other side. ,he lens is formed !ycutting it long principal axis into two e4ual parts and are 6oined as indicated in column ''.Co !mn I Co !mn II

A Plane of image move towards screen if G f G is increased p#mall portion of each part near pole isremoved. ,he remaining parts are 6oined

* 'mages formed will !e virtual 4,he two parts are separated slightly. ,he gapis filled !y opa4ue material

#eparation !etween image increases if G u G decreases r,he two parts are separated slightly. ,he

gap is filled !y opa4ue material.

7


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'nterference pattern can !e o!tained if screen is ssuita!ly positioned #mall portion of each part near pole is

removed. ,he remaining parts are 6oined.#ol$ A p54H * p545r5sH 5 H r s p

onceptual

Pa##a$e : II,he I #J apparatus is modified !y placing an isotropic transparent plate of high melting point

in front of one of the slits. ,he refractive index of the plate is r 1."=m at room temperature and

its thic


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#ol$ *#%&. #o5 the num!er of crossed fringes5

( )2 1 tn-m m

=

l- -

@

1." 2 10 10 2 10- 10

- -

-

=

710

-

=

1@. A narrow monochromatic !eam of light of intensity ' is incident on a glass plate as shown infigure. Another identical glass plate is


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1 1 1 y x f

=

fx y

f x=

2

dy f dxdx f x dy

= 2

1 2 2 f f

V g x f x =

or B 1 to !e maximum1 0

dV dT

=

3 f

x =

( )1V maximum 3

37

fg =

Pa%a$%a&' (o% )!e#t*on# No#. 1+ to 21

igure shows a convex lens of focal length 12cm lying in a uniform magnetic field of * ofmagnitude 1.2 , parallel to its principle axis. A particle having a charge 32 10 C and mass

"2 10


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#%&.3

21=

V m

u= = =

image object r m r = 2 7 =cm= = .

22. A watch glass has uniform thic


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#ol$ ?>,-" #%&-9'&2 . #ome optical components are given in olumn '. ,he values of lateral magnification are listed in

olumn ''. atch all the possi!le magnification values from olumn '' with the appropriatecomponent in olumn '. 'ndicate your answer NNN. .Co !mn A Co !mn ,

A oncave mirror p 2

3

+* onvex mirror 4 3

2+

onvex lens r 23

oncave lens s 3

2

#ol$ ?>,-" #%&-9'&2@. A convex lens of focal length 1" cm is

split into two halves and the two halvesare placed at a separation of 120 cm.*etween the two halves of convex lens a

plane mirror is placed hori;ontally andat a distance of 7 mm !elow the

principal axis of the lens halves. Ano!6ect A* of length 2 mm is placed at adistance of 20 cm from one half lens asshown in figure.

f . 1 " c m

7 m m2 0 c m

2 m m

1 2 0 c m

f . 1 " c m

A

*

,he final image of the point A is formed at a distance ofn

mm3

from the principle axis.

etermine the value of n.#ol$ ?>,-" #%&-9'&

2=. #,A,J J9, ? ' $- ,he mirage is not only formed in hot desert !ut it is also formed in a very

cold region called looming .

#,A,J J9, ? '' $ - ,he total internal reflection ta


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2C. ,he position of central maxima at , 0 from the point % is

a 1.= mm ! 3. mm c @.2 mm d 17.7 mm

#ol$

30. ,he time when central maxima reaches % is

a 1#ec ! 2#ec c 3#ec d 7#ec

#ol$

31. O#peed of the central maxima when it is at % is

a 32 10 /m s ! 33 10 /m s c 37 10 /m s d 3" 10 /m s#ol$ *

2+ / 1 #%& . ( )1 1l air l sair P P t t = +

( )1 2 air yd

s p s p D

=

1q

l

tD y

d

=

7

10

tD T y

d T

=

20

" Dt

y T d = =

Belocity v ( ) 210dy Dt dt d T

=

I 0 at , 7sec

32. A dou!le convex lens forms a real image of an o!6ect on a screen which is fixed. 9ow the lens is

given a constant velocity 1 m/s along its axis and away from the screen. or the purpose offorming a sharp image always on the screen5 the o!6ect is also re4uired to !e given an appropriate

velocity. ,he velocity of the o!6ect at the instant the si;e of the image is half the si;e of the

o!6ect.

a 1 m/s ! 2 m/s c 3 m/s d 7 m/s

#ol$

#%&. 2/ /i l o l v m v=

211o l v v m= uu uv v

10


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33. ,wo spherical mirrors one convex and other concave are each of same radius r. ,hey are co-axiallyarranged at a distance 2 r from each other. A small portion in the form of circle of radius (a) is cutout from convex mirror near the pole.

A radius of 1st image of hole is%3

* radius of second image of hole is%

11

image distances for the second image is 6 11

difference in radii !etween 1 st and 2 nd image is.%33

#ol$ A5*5#%&. :eflection from 2m

11

1 1 2 2 v

v 2 3+ = =

agnification 11v 1

m

u 3

= =

:adius of 1 st image 1 % / 3=:eflection at convex

O1 O2

M1 M2

2

istance from convex mirror 2 4

2 3 3

=

2f 3 3 % %

mu f 11 11 3 11

= = = =

37. STATE"ENT1A dou!le convex lens made of material of :' 1 is placed inside two

li4uids of :' 2 and 3 as shown in fig. 2 1 3 > > . A wide parallel !eam of light is incident on lens from left. ,he lower halfwill give rise to a convergent !eam and upper half of lens willgive rise to a divergent !eam.

12

3

STATE"ENT2'f a lens is immersed in li4uid. ,he focal length would change.

#ol$ *

3". ,he refractive index of the medium within a certain region50 0,> > changes with y. A thin light ray travelling in the x-direction stri


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#%&. *y #nell)s law#!i# &'#! "%#" =At 0 0) 0, 0 ,# #= = =

( ) 00# ) !i# # !i# 0 =

4

Y

P

(R5 )

( ) ( ) ( ) ( )0R )

# # ) !i# # ) R

= =( ) 0# ) #>

,he material with the greatest


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- R 2!i#i - 10 3 1. &m

R 3= = +

3=. At what distance a second identical rod !e placed on the mirror such that emergent ray from thesecond rod is in line with incident ray on 1 st rod.

A 21." cm * 31." cm 11." cm 71." cm

#ol$ *

#%&. or the ray to retrace path in second glass rod with centre 2O( )1 2O O 2 R= +

R 10"%#i

3= =

1 210

O O 2 203

= +

3C. eviation suffered !y ray in second rod is

A0

30 *0

40; 060#ol$#%&. rom fig

( )2 i = since the emergent ray from the second rod is in line with the incident ray on 1 st rod.( ) 02 60 30 60 = =

70. ,he image of a small real o!6ect placed perpendicular to the optical axis is erect and smaller thano!6ect in si;e.1 concave lens 2 convex lens 3 concave mirror 7 convex mirror

#ol$ 1#%&. *asic concept.71. ,he radius of curvature of each surface of an e4ui convex lens is 72 R cm= . :efractive index of

the glass 1.2"= . 'f the final image forms after four internal reflections inside the lens for paraxial incident !eam calculate the distance of the image from the lens.

So : 7#%&. #olving for each reflection we get

distance from the pole of the lens.

( ) ( )

727 .

2 1 2 7 1.2" 1.2" 1n

Rcm

= = =+ +

2. A !lac< spot B is mar


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SOL. ,o satisfy the conditionsr C

and r C A r L r 2C 2 sin ?1 2/3 d

Q Q Q

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PHYSICS 08-11-11 Assgnament With Solutions

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