optics f 1 ass 1 (2)

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ASSIGNMENTS

SUBJECTIVE

LEVEL -I

1. White light is used in a Young's double slit experiment. Find the minimum order of the violetfringe ( λ = 400 nm) hi!h overlaps ith a red fringe ( λ = "00 nm).

#. $n a double slit interferen!e experiment% the separation bet een the slits is 1.0 mm% theavelength of light used is &.0 x 10 " m and the distan!e of the s!reen from the slits is 1.0 m.

(a) Find the idth of the !entral maximum.(b) o man bright fringes are formed in one !entimeter idth on the s!reen*

+. , plate of thi!-ness t made of a material of refra!tive index µ is pla!ed in front of one of the

slits in a double slit experiment.(a) Find the !hange in the opti!al path due to introdu!tion of the plate.(b) What should be the minimum thi!-ness t hi!h ill ma-e the intensit at the !entre of

the fringe pattern ero* Wavelength of the light used is λ. /egle!t an absorption of lightin the plate.

4. he idth of one of the t o slits in a Young s double slits experiment is double of the other slit. ,ssuming that the amplitude of the light !oming from a slit is proportional to the slit

idth% find the ratio of the maximum to the minimum intensit in the interferen!e pattern.

&. , long narro hori ontal slit is pla!ed 1 mm above a hori ontal plane mirror. heinterferen!e bet een the light !oming dire!tl from the slit and that after refle!tion is seen on

a s!reen 1.0 m a a from the slit. $f the mirror refle!ts onl 243 of the light energ falling onit% hat ill be the ratio of the maximum to the minimum intensit in the interferen!e patternobserved on the s!reen*

2. , rod of length 10 !m lies along the prin!ipal axisof a !on!ave mirror of fo!al length 10 !m in su!ha a that the end !loser to the pole is #0 !ma a from it. Find the length of the image.

FA B

10 cm 20 cm

". he refra!tive index of the material of a prism of refra!ting angle 4& 0 is 1.2 for a !ertainmono!romati! ra . What ould be the minimum angle of in!iden!e of this ra on the prismso that no total internal refle!tion ta-es pla!e. ,s ra s !omes out of the prism.

( in 1

5

& = +5 °40 % sin20°#0 = 0.11% sin10 °40 = 0.1"2)

5. ,n astronomi!al teles!ope has an ob6e!tive of fo!al length 100 !m and an e epie!e of fo!allength #0 !m. he diameter of the ob6e!tive is & !m. Find the magnif ing po er in normalad6ustment.

7. , point sour!e is pla!ed mid abet een t o !onverging mirrors havinge8ual fo!al length f as sho n in figure.Find the values of d for% hi!h onl onimage is formed.

d

FIITJEE , ICES HOUSE (Opp. VIJAY MANDAL ENCLAVE), SARVAPRIYA VIHAR, NEW DELHI 1!. P"#!$%&102, !$!%1$2, FA'# !%1 &2

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LEVEL - II

1. $n a Young s double slit experiment a parallel light beam !ontaining avelength λ1 = 4000 , °and λ# = &200, ° is in!ident on a diaphragm having t o narro slits. eparation bet een the

slits is d = #mm. $f distan!e bet een diaphragm and s!reen is > = 40 !m% !al!ulate(a) distan!e of first bla!- line from !entral bright fringe and(b) distan!e bet een t o !onse!utive bla!- lines.

#. White !oherent l ight (400 nm "00 nm) issent through the slits of a Young's double slitexperiment (fig.). he seperation bet eenthe slits is 0.& mm and the s!reen isobserved at a point 1.0 mm a a (along the

idth of the fringes) from the !entral line.

(a) Whi!h avelength(s) ill be absent in thelight !oming from the hole*

(b) hi!h avelength(s) ill have a strongintensit *(a = 0.& mm@ b = 1.0 mm)

0.%mm

1mm

%0 cm

+. , thin paper of thi!-ness 0.0# mm having a refra!tive index 1.4& is pasted a!ross one of theslits in a Young s double slit experiment. he paper transmits 4;7 of the light energ falling onit.

(a) Find the ratio of the maximum intensit to the minimum intensit in the fringe pattern.(b) o man fringes ill !ross through the !entre if an identi!al paper pie!e is pasted on

the other slit also* he avelength of the light used is 200 nm. 4. , right prism is to be made b sele!ting a proper

material and the angles , and A (A ≤ ,)% as sho nin figure. $t is desired that a ra of light in!identnormall on ,A emerges parallel to the in!identdire!tion after t o total internal refle!tions.

(a) What should be the minimum refra!tive index µ for this to be possible *

(b) For µ = &;+% is it possible to a!hieve this ith theangle , e8ual to 20 degrees *

A

θ

θ

C B

&. , !onvex lens fo!uses a distant ob6e!t on a s!reen pla!ed 10 !m a a from it. , glass plate

(µ = 1.&) of thi!-ness 1.& !m is inserted bet een the lens and the s!reen. Where should theob6e!t be pla!ed so that its image is again fo!used on the s!reen*

2. , bi!onvex thin lens is prepared from glass ( µ = 1.&)% the t o bounding surfa!es havinge8ual radii of #& !m ea!h. ?ne of the surfa!es is silvered from outside to ma-e it refle!ting.Where should an ob6e!t be pla!ed before this lens so that the image is formed on the ob6e!titself *


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". , point ob6e!t is pla!ed at a distan!e of 0.+m froma !onvex lens (fo!al length 0.#m) !ut into t ohalves ea!h of hi!h is displa!ed b 0.000&m assho n in the figure. Find the position of theimages. $f more than one image is formed% findtheir number and the distan!e bet een them

O 0.0005 m

5. , thin bi!onvex lens of refra!tive index +;# is pla!ed on ahori ontal plane mirror as sho n in the figure. he spa!ebet een the lens and the mirror is then filled ith ater of refra!tive index 4;+. $t is found that hen a point ob6e!t ispla!ed 1&!m above the lens on its prin!iple axis% the ob6e!t!oin!ides ith its o n image. ?n repeating ith another li8uid% the ob6e!t and the image again !oin!ide at a

distan!e #& !m from the lens. 9al!ulate the refra!tiveindex of the li8uid.

7. o !oherent narro slits emitting light of avelength λ in the same phase are pla!ed parallel

to ea!h other a small separation of # λ. he light si!olle!ted on a s!reen ∑ hi!h is pla!ed at adistan!e > (BB λ) from the slits 1 as sho n infigure. Find the distan!e x su!h that the intensit at< is e8ual to the intensit at ?.

<#λ

>

#1∑

?

10. , !onverging lens of fo!al length 1& !m and a!onverging mirror of fo!al length #0!m are pla!edith their prin!ipal axis !oin!iding. , point sour!e is

pla!ed on the prin!ipal axis at a distan!e 1#!m fromthe lens as sho n in the figure. $t is found that thefinal beam !omes out parallel to the prin!ipal axisfind the separation bet een the mirror and the lens.

4•

1# !m

11. , ra of light is in!ident on the surfa!e of a

transparent sphere of refra!tive index#

". ,fter

refra!tion it is refle!ted and refra!ted out of sphereagain. >etermine the value of the angle of in!iden!eand deviation to the nearest degree so that thedeviation ma be minimum. (sin 4" °= √+;")

1 # +

1#. , !ubi!al blo!- of glass (refra!tive index µ = 1.&) has a!on!entri! spheri!al !avit of radius r = +!m. Ca!h edgeof the !ube is = 1#!m long. , luminous point ob6e!t isat a distan!e a = 1#!m on left of left fa!e of the !ube assho n in figure. 9al!ulate apparent position of the ob6e!t

hen seen from right side of the !ube

= 1#

a = 1#

r


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PH - OP - 53

1+. , thin plano !onvex lens made of glass ( µ = 1.&) splitinto t o halves. ?ne of the halves is shifted along theopti!al axis as sho n in figure. he separation bet eenfixed luminous point ob6e!t ? and fixed s!reen is > = 150!m. he magnifi!ation of image formed b one of the half lenses is m =#. 9al!ulate fo!al length f of the lens andseparation bet een t o half lenses.

?

> = 150 !m

s!reen

?ne of the t o half lenses is removed and one surfa!e of the other half lens is silvered. /othis half lens is moved along the opti!al axis so that a sharp image of ob6e!t is again formedon the s!reen. 9al!ulate distan!e of this half lens from ob6e!t ? at this instant.

14. he figure sho s t o !oherent sour!es 1 and # hi!h emit lightof avelength λ in phase. he separation bet een the sour!es is+λ. , !ir!ular ire of large radius is pla!ed in su!h a a that 1 #is at the !entre of the ire. Find the angular position θ on the ire

for hi!h !onstru!tive interferen!e ta-es pla!e.

#1

θ

1&. he refra!tive indi!es of the !ro n glass for blue and red lights are 1.&1 and 1.47respe!tivel and those of the flint glass are 1."" and 1."+ respe!tivel . ,n isos!eles prism of angle 2 0 is made of !ro n glass. , beam of hite light is in!ident at a small angle of thisprism. he other flint glass isos!eles prism is !ombined ith the !ro n glass prism su!h thatthere is no deviation of the in!ident light. >etermine the angle of the flint glass prism.9al!ulate the net dispersion of the !ombined s stem.


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5. When the distan!e bet een the ob6e!t and the s!reen is more than 4f% e !an obtain theimage of the ob6e!t on the s!reen for the t o positions of the lens. $t is !alled displa!ementmethod. $n one !ase the image is magnified. $f $ 1 and $ # be the si es of the t o images% thenthe si e of the ob6e!t isE(,) ($ 1 $#);# (A) $1 − $#(9) √($1 $#) (>) √($1;$#)

7. $n the displa!ement method% a !onvex lens is pla!ed in bet een an ob6e!t and a s!reen. $f the magnifi!ation in the t o positions be m 1 and m # and the displa!ement of the lensbet een the t o positions is G% then the fo!al length of the lens is E(,) G;m 1 × m #) (A) G;(m 1 − m #)(9) G;(m 1 m #) (>) G;(m 1 − m #)#

10. , !onvex lens of fo!al length f is pla!ed in bet een a real ob6e!t and a s!reen. he distan!ebet een the ob6e!t and the s!reen is G. $f the numeri!al value of the magnifi!ation produ!ed

b the lens is m% then the fo!al length of the lens is E(,) mG;(m 1) # (A) mG;(m −1) #(9) (m 1) #;mG (>) (m − 1)G;m

11. , ra of light passes through an e8uilateral prism. (refra!tive index = 1.&) su! h that theangle of in!iden!e is e8ual to the angle of emergen!e and later is e8ual to +;4 th the angle of prism. he angle of deviation is E(,) 4& o (A) +7 o

(9) #0 o (>) +0 o

1#. , thin prism < 1 ith angle 4 o and made from glass of refra!tive index 1.&4 is !ombined ith

another thin prism < # made from glass of refra!tive index 1."# to produ!e dispersion ithoutdeviation. he angle of the prism < # is E(,) &.++ o (A) 4 o

(9) + o (>) #.2 o

1+. Fo!al lengths of t o lenses are f and f and dispersive po ers of their materials are ω . oform a!hromati! !ombination from these% hi!h relation is !orre!t*(,) ω = ω0%ω = #ω0% f = #f (A)ω = 0%ω = #ω0% f =−#f (9) ω = ω0%ω = #ω0% f =f;# (>)ω = ω0%ω = #ω0% f =−f;#.

14. For hi!h !olour the angle of deviation is the least*(,) Hiolet (A) Alue(9) :ed (>) Yello

1&. , li8uid is pla!ed in a hollo prism of angle 20 o. $f angle of the minimum deviation is +0 o%hat is the refra!tive index of the li8uid*

(,) 1.41 (A) 1.&0(9) 1.2& (>) 1.7&


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PH - OP - 56

LEVEL-II

1. he fo!al lengths of a !onvex lens for blue and red !olours of light are f b and f r respe!tiveland those of a !on!ave lens are F b and F r . hen@(,) f b B f r and F b D F r (A) f b D f r and F b B F r (9) f b B f r and F b B F r (>) f b D f r and F b D F r

#. , !onvex lens% a glass slab% a glass prism and a spheri!al solid ball have been preparedfrom the same opti!all transparent material. >ispersive po er ill be possessed b E(,) the glass slab and the prism (A) the lens and the solid ball(9) the prism onl (>) all the four

+. , beam of light !onsisting of red% green and blue!olours is in!ident on a right angled prism. herefra!tive indi!es of the material of prism for the abovered% green and blue avelengths are 1.+7% 1.44 and1.4" respe!tivel . he prism illE 4& o

(,) separate part of the red !olour from the green and blue !olours(A) separate part of the blue !olour from the red and green !olours(9) separate all the three !olours from one another (>) not separate even partiall an !olour from the other t o !olours.

4. , prism !an produ!e a minimum deviation δ in a light beam. $t three su!h prisms are!ombined% the minimum deviation that !an be produ!ed in this beam isE(,) 0 (A) δ(9) # δ (>) + δ

&. , beam of hite light is in!ident on a hollo prism of glass. hen E(,) he light emerging from prism gives no spe!trum(A) he light emerging from prism gives spe!trum but

the bending of all !olours is a a a from base.(9) he light emerging from prism gives spe!trum% all the

!olours bend to ards base% the violet most and redthe least.

(>) he light emerging from prism gives spe!trum% all the

!olours bend to ards base% the violet the least andred the most.

i

Whitelight

2. ,n e8uilateral triangular prism is made of glass ( µ = 1.&). , ra of light is in!ident normall onone of the fa!es. he angle bet een the in!ident and emergent ra is E(,) 20 o (A) 70 o

(9) 1#0 o (>) 150 o

". , prism of refra!tive index µg deviates the in!ident ra to ards it base. $f it is immersed in atransparent li8uid of refra!tive index µ su!h that µ B µg then the prism ouldE(,) >eviate the ra to ards its base (A) >eviate the ra a a from its base

(9) /ot deviate the ra at all (>) /othing !an be said


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5. , thin prism of glass is pla!ed in air and ater su!!essivel . $f aµg = +;# andaµ = 4;+% then the deviation produ!ed b the prism for a small angle of in!iden!e henpla!ed in air and ater is E(,) 7 E 5 (A) 4 E +

(9) + E 4 (>) 4 E 1

7. he angle of a prism is +0 o. he ra s in!ident at 20 o on one refra!ting fa!e suffer a deviationof +0 o. hen the angle of emergen!e is E(,) 0 o (A) +0 o

(9) 20 o (>) 70 o

10. < is a small angled prism of angle + o made of a material of refra!tive index 1.&. , ra of light is in!ident as sho n infigure. I is a plane mirror. he angle of deviation for thera refle!ted from the mirror I ith respe!t to the in!ident

ra is E(,) 4.& o (A) 1"&.+ o

(9) 1"" o (>) 1"5.& o I<

11. he fa!e ;d (A) λd;>(9) d; λ> (>) >; λd

14. o !oherent mono!hromati! light beams of intensities $ and 4$ are superposed. hemaximum and minimum possible intensities in the resulting beam areE(,) & $ and $ (A) 7 $ and $(9) & $ and + $ (>) 7 $ and + $

1&. $n Young s double slit experiment the " th maximum ith avelength λ1 is at a distan!e d 1 andthat ith avelength λ# is at distan!e d #. hen d 1;d # is(,) λ1;λ# (A) λ#;λ1(9) ##

#1 ; λλ (>) #1## ; λλ


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PH - OP - 5

KANS!E"S

SUBJECTIVE

LEVEL - I

1. "#. (a) 0. & mm (b) #0

+. (a) ( µ 1)t (b) ( )1# −µλ

4. 7&. 51 E 12. 1& !m from pole% image length e8uals & !m". minimum value of i = 10 0 5'5. &7. #f% 4f

10. (a)

+µ

#1

above itself%

+µ

#+

belo itself

(b)

µ+

#

11 belo itself%

µ+

#

+1 belo itself

11. #2." !m

1#. $mage ill form at ob6e!t itself.

1+. (a) ero (b)d4

>>d

d4## λ≅+λ hen d D D >

14. #0 !m

1&. 45

LEVEL - II

1. (a) #50 µm (b) &20 µm #. (a) 400 nm% 22" nm (b) &00 n m

+. (a) #& (b) 1&

4. (a) µ ≥ 2 (b) otal internal refle!tion does not ta-es pla!e at one of the surfa!e.

&. 170 !m from the lens. 2. 1#.& !m

". v = 0.2 m% d = 0.00+ m 5. 1.2

7. √+> 10. #& !m.

11. r = 41 °% 1+2° 1#. 7 !m

1+. f = 40 !m% (b L a) = 20 !m

14. θ1 = 70 o %θ# = 45.# o%θ+ = "0.& o %θ4 = 0 o and points s mmteri!all lo!ated in other8uadrants.

1&. 40% 0.040


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OBJECTIVE

LEVEL- I

1# B 2# B

3# A 4# B$ %

5# B 6# %

7# C # C

9# B 10# A

11# % 12# C

13# B 14# C

15# A

LEVEL- II

1# % 2# %

3# A 4# B

5# A 6# C

7# % # %

9# A 10# %

11# A 12# %

13# C 14# B

15# A


optics f 1 ass 1 (2)

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