Notes n Ques

8/17/2019 Notes n Ques

1/61

Mohammed

Asif

Name :

Roll No. :

Topic : Optics

Ph : 9391326657, 66!6657

Teachi"# Notes $Optic%

• The st&d' of li#ht a"d (isio" is called optics.• )i#ht is a fo*m of e"e*#' +hich is p*opa#ated as lect*oma#"etic +a(es +hich p*od&ces the

se"satio" of si#ht i" &s.

• -eomet*ical optics t*eats p*opa#atio" of li#ht i" te*ms of *a's a"d is (alid o"l' if +a(ele"#th of

li#ht m&ch lesses tha" the sie of o/stacles.

i% )i#ht does "ot *e0&i*e a medi&m fo* its p*opa#atio"

ii% ts speed i" f*ee space $(acc&m% is 3 1!4

msiii% t is t*a"s(e*se i" "at&*e

• " the spect*&m of e.m.+. it lies /et+ee" &.(. a"d i"f*a*ed *e#io" a"d has +a(ele"#th /et+ee"!!! to 7!!!

O

A . i.e( )mtom µ µ 7.04.0

"di#o is "ot diste"si/le f*om /l&e.

A8 ;NATON8

• 8o&*ce:A /od' +hich emits li#ht is called so&*ce. 8o&*ce ca" /e a poi"t o"e $o*% ete"ded o"e.

$a% 8elfl&mi"o&sso&*ce: The so&*ce +hich possess li#ht of it o+".

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 1

$h% 040 #4#0##"7, '3'13(##"7. ))).asi*iitphsics.vriti.co+

http://www.asifiitphysics.vriti.com/http://www.asifiitphysics.vriti.com/


2/61

: 8&", lect*ic a*c, a"dle, etc.

$/% No"l&mi"o&s8o&*ce: t is a so&*ce of li#ht +hich does "ot possesses li#ht of its o+" /&t acts as

so&*ce of li#ht /' *eflecti"# the li#ht *ecei(ed /' it.

: Moo", o/


3/61

• ?i*t&al O/


4/61

The di*ectio" of i"cide"t e"e*#' is called i"cide"t *a' a"d the di*ectio" i" +hich e"e*#' is

th*o+" /ac= is called *eflected *a'. t is of t+o t'pes.

• )A8 O; R;)TON:1% ;i*st )a+: The i"cide"t *a', the *eflected *a' a"d the "o*mal to the *eflecti"# s&*face at the

poi"t of i"cide"ce, all lie i" o"e pla"e +hich isr ⊥ to the *eflecti"# s&*face.

2% The a"#le of i"cide"ce is e0&al to the a"#le of *eflectio" r i ∠=∠ .Note:

1% The la+s of *eflectio" a*e (alid fo* a"' smooth *eflecti"# s&*face i**especti(e of #eomet*'.

2% he"e(e* *eflectio" ta=es place, the compo"e"t of i"cide"t *a' pa*allel to *eflecti"# s&*face*emai"s &"cha*#ed, +hile compo"e"t pe*pe"dic&la* to *eflecti"# s&*face $i.e. alo"# "o*mal%

*e(e*se i" di*ectio".

---

1 k z j yi xr ++=

→

,

---

( k z j yi xr −+=

→





5/61

3% ?ecto* fo*m of la+s of Reflectio":

-----

.( N N I I R

−=→ R B"it (ecto* alo"# the *eflected *a'

→-

I B"it (ecto* alo"# the "cide"t *a'

→

-

N B"it (ecto* alo"# the "o*mal *a'

• ma#e fo*med /' a pla"e mi**o*:a% Poi"t 8o&*ce: ;o* co"st*&ctio" of ima#e of a poi"t so&*ce it is s&fficie"t to co"side* a"' t+o

*a's falli"# o" mi**o*. The poi"t of i"te*sectio" of co**espo"di"# *eflected *a's #i(e the

positio" of ima#e as sho+" i" fi#&*e.

OA C A

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". "




6/61

( ) ABI ABD ∆≅∆∴ma#e lies as m&ch /ehi"d the mi**o* as the o/


7/61

ases: he" i C ! $No*mal i"cide"ce%

π δ =+a

he"(

π =i $-*ai"# i"cide"ce%

0+i/ =δ

M&ltiple Reflectio":

∑= inet δ δ iδ C de(iatio" d&e to si"#le *eflectio".Note +hile s&mmi"# &p, se"se of *otatio" is ta=e" i"to acco&"t.

D: 1% T+o pla"e mi**o* a*e i"cli"ed to each othe* s&ch that a *a' of li#ht i"cide"t o" the fi*st mi**o*

a"d pa*allels to the seco"d is *eflected f*om the seco"d mi**o* pa*allel to the fi*st mi**o*.

ete*mi"e the a"#le /et+ee" the t+o mi**o*. Also dete*mi"e the total de(iatio" p*od&ced i" the

i"cide"t *a' d&e to the t+o *eflectio"s.

8ol&tio":

;*om fi#&*e 103 =θ 0

#0=θ i(

1 −=π δ

↑=×−= 1(030(10 0 A...00

( 1(030(10( =×−=−= iπ δ ( ) ↓↑=+=∴ 1(0(40

1( or net δ δ δ

O* ;*om fi#. #01010 +=+= θ δ ( ) ↓↑= 1(0(400 or





8/61

D: 2% alc&late de(iatio" s&ffe*ed /' i"cide"t *a' i" sit&atio" as sho+" i" fi#&*e, afte* th*ee

s&ccessi(e *eflectio"sE

8ol&tio": ;,.

i(

1 −=π δ

↑=×−= 100"0(10 0

↓=×−= 00(

140(0(10δ

↓=×−= 00(

1#010(10δ

( ) ↓↑=↓+↓+↑= 0

(#01001#0140100 or net δ

D: 3% T+o pla"e mi**o*s a*e i"cli"ed to each othe* at a" a"#le . A *a' of li#ht is *eflected fi*st at

o"e mi**o* a"d the" at the othe*. ;i"d the total de(iatio" of the *a'E

8ol&tio": )et =α A"#le of i"cide"ce fo* M1=β A"#le of i"cide"ce fo* M2=

1δ e(iatio" d&e to M1=

(δ e(iatio" d&e to M2

;*om fi#&*e

α π δ (1 −= β π δ ((

−=Also *a' is *otated i" same sec&*e $i.e.% a"ticloc=+ise

(1 δ δ δ += Net No+ i" OBC ∆

β π α π (( −+−= 010=∠+∠+∠ COB BCOOBC

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#".




9/61

( )β α π δ +−= (( Net ( ) ( ) 000 10'0'0 =+−+− θ β α ( )θ π δ (( −=∴ Net θ β α =+

θ π δ (( −= Net

• ?elocit' of ma#e:)et

Om C coo*di"ate of o/


10/61

Note: f the (elocit' of the o/


11/61

( ) ( ) smV I 10#(((1 −=−−=∴ ⊥;o* compo"e"t of (elocit' of ima#e pa*allel to the mi**o*

( ) smV I

11 =∴ ?elocit' of time ( ) ( )((

1 n I I I V V V +=

m1#4#4100 =+=

=∴ −"

4ta/

1θ

D: 3% T+o pla"e mi**o* a*e placed as sho+" i" the fi#&*e /elo+:

A poi"t o/


12/61

( IM V →

is #i(e" /' the (ecto* s&m of compo"e"ts of (elocit' of ima#e +.*.t. M2 alo"# the "o*mal

a"d r 1⊥ to the "o*mal.

→ -00

-0(

-00

-0(

3c3s13c o1 03 7c o3 7s i /1 0 03 7s i /1 0 0(

ji jiV I M

sc ji 14 0( 0--

+−=

1(1( , IM IM IM IM V V V →→→

−=

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 1(




13/61

s4 01 ( 0

--

c m ji

+−=

D: % " the sit&atio" sho+ i" fi#&*e, fi"d the (elocit' of ima#eE

8ol&tio": Alo"# F di*ectio", appl'i"#

( )mmi V V V V −−== 0

( ) ( )000 30cos"#0cos1030cos" −−−=−−i

V

( ) smiV i

31"

-

+−=∴

Alo"# 'di*ectio" ?! C ?i

sm jV i "# 0s i /1 0

-0

==∴

∴ ?elocit' of the ima#e ( ) sm ji "31"--

++−=

D: 5% A" o/


14/61

0V V V V

mmi −=−

( ) ( ) "11 −−=−−iV sm smV i 77 ⇒−= a"d di*ectio" to+a*ds left.

D: 6% ;i"d the *e#io" o" 'ais i" +hich *eflected *a's a*e p*ese"t o/


15/61

++

−

-0

-0

-0

-0

#s#c o# 0s i /# 0c o s jV iV jV iV

D: 4% A *a' of li#ht ma=i"# a"#le 2!! +ith the ho*io"tal is i"cide"t o" a pla"e mi**o* +ith itself

i"cli"ed to the ho*io"tal at a"#le 1!!

, +ith "o*mal a+a' f*om the i"cide"t *a'. hat is thea"#le made /' the *eflected *a' +ith the ho*io"talE

8ol&tio": AO C "cide"t *a'

O C Reflected *a'

The *eflected *a' #oes alo"# the ho*io"tal. @e"ce a"#le made /' the *eflected *a' +ith the

ho*io"tal is e*o.

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 1"




16/61

D: 9% A *a' of li#ht ma=i"# a"#le 1!! +ith the ho*io"tal is i"cide"t o" a pla"e mi**o* ma=i"# a"#le

+ith the ho*io"tal. hat sho&ld /e the (al&e of , so that the *eflected *a' #oes (e*ticall'

&p+a*dsE

a% 3!! /% !! c% 5!! d% 6!!

8ol&tio":

• N&m/e* of ma#es ;o*med /' t+o "cli"edPla"e Mi**o*s:a% he" mi**o* a*e pa*allel: " this case, i"fi"ite ima#es a*e fo*med d&e to m&ltiple *eflectio"s.

/% he" mi**o* a*e pe*pe"dic&la*: " this case, th*ee ima#es a*e fo*med. The *a' dia#*am is

sho+".

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 1#




17/61

Note that the thi*d ima#e is fo*med d&e to *a's &"de*#oi"# t+o s&ccessi(e *eflectio". Also,

o/


18/61

$a% The ima#e +ill appea* to /e at *est +.*.t. the pa*ticle at the i"sta"t, the (elocit' of the

pa*ticle is pa*allel to the mi**o*.

θ ta/= x

y

V

V

θ α

α ta/

cos

si/=

−V

gt V

( )

g

V t

θ α α ta/ta/cos −=

$/% 8t. li"e r 1⊥ to mi**o*

D: 2% A" a o/lo"# o/


19/61

D: 3% A pla"e mi**o* is placed at pa*allel of 'ais, faci"# the positi(e ais. A" o/


20/61

D: 5% A *a' is t*a(eli"# alo"# ais i" "e#ati(e di*ectio". A pla"e mi**o* is placed at o*i#i" faci"#

the *a'. hat sho&ld /e the a"#le of pla"e mi**o* +ith the ais so that the *a' of li#ht offe*

*eflecti"# f*om the pla"e mi**o* passes th*oh poi"t $1m, m3 %E

8ol&tio":

D: 6% T+o pla"e mi**o* A a"d a*e ali#"ed pa*allel to each othe* as sho+" i" the fi#&*e. A li#ht *a'

is i"cide"t at a" a"#le 3!! at a poi"t


21/61

• 8i#"o"(e*sio":

• R&les fo* Ra'ia#*ams1% A *a' of li#ht pa*allel to p*i"cipal ais passes $o*% appea*s to pass th*oh fo&* afte*

*eflectio".

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". (1




22/61

2% A *a' of li#ht passi"# th*oh foc&s $o*% appea*s to pass th*oh foc&s /ecomes pa*allel to

p*i"cipalais afte* *eflectio".

3% A *a' of li#ht passi"# th*oh $o*% appea*s to pass th*oh ce"t*e of c&*(at&*e is *eflected

/ac=.

% A *a' of li#ht hitti"# pole is *eflected ma=i"# e0&al a"#le +ith p*i"cipal ois

Note: 1% ;ocal le"#th a"d *adi&s of c&*(at&*e of pla"e mi**o* C α 2% o"ca(e mi**o* C o"(e*#e"t mi**o*

o"(e mi**o* C i(e*#e"t mi**o*

• Relatio" /et+ee" focalle"#th a"d *adi&s of c&*(at&*e:

=

(

R " oth fo* co"ca(e a"d co"(e mi**o*.

• Mi**o* fo*m&la $o*% Mi**o* 0&atio":The *elatio" /et+ee" u, v a"d f of a mi**o* is ="o+" as mi**o* fo*m&la

+=

$% " 111

• Relatio" /et+ee" the speeds of o/


23/61

" $%

111 =+ >>>.$1%

iffe*e"tiati"# /oth sides +.*.t. time $t%, +e #et

0.1

.1

(( =−−

dt

d$

$dt

d%

%

0.1

.1

(( =−=

dt

d$

%dt

d$

$

dt

dy

%

$

dt

d$.

(

(

−= >>>>$2%

8i"ce timeo" s&eed $dt

d$i ==

object o" s&eed $dt

d%==

0

0

(

.$%

$$i

=∴ >>>>.$3%

;*om e0&atio" $1%,

( ) " x

"

%

$or

" %

" %$

−=

−=

@e"ce e0&atio" $2% /ecome

0.$ " %

" $i

−

−=

• )i"ea* ma#"ificatio": t is defi"ed as the *atio of the sie $o*% hei#ht of the ima#e to the sie $o*%hei#ht of the o/


24/61

%

$

O

I

−−

=+−

%

$

O

I −=

−=∴

%

$m same fo* co"(emi**o* also.

• Ma#"ificatio" i" te*ms of &, ( a"d f a% As +e ="o+ that

" $%

111=+

M&ltipl'i"# /oth sides /' H& +e #et

"

%

$

%

%

%=+

"

%

$

% =+1

"

" %

"

%

$

% −=−= 1

" %

"

m

$

−=∴

8i"ce%

$m −=

( )

−

=−

−=∴% "

" mor

" %

" m

/% As +e ="o+ that " $%

111=+

M&ltipl'i"# /oth sides /' ?, +e #et

"

$

$

$

%

$ =+

"

$

%

$ =+1

"

" $

"

$

%

$ −=−= 1

8i"ce%

$m −=

( ) "

$ " mor

"

" $ −=

−−=

Note: a% G(e ma#"ificatio" mea" /oth o/


25/61

;o* ete"ded o/


26/61

D: 1% ;i"d the (elocit' of ima#e i" sit&atio" as sho+" i" fi#&*eE

8ol&tio": smiiiV 1 1('

---

0 =

+=→

-

( iV m

−=→

ms

( ) (

30(0

(0−=

−−−−

=−

=∴% "

" m

( )11

(

11

−=∴

→

M O M I V mV

C $2%2 11-

i

C -

ims.

( ) I

m I

n

m I m I V V V + =∴ −−

( ) sm j x (41(( −=−−=

I

m I

n

m I

n

m I V V V

+

=

∴

−−−

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". (#




27/61

sm ji 1( 44 4--

−−=

--

(( 44 4 i jiV V V mm I I =

−−==

=

→→−

−−= →

ji (4 #-

D: 2% A thi" *od of le"#th3

" is placed alo"# the p*i"cipal ais of a co"ca(e mi**o* of focalle"#th Hf

s&ch that its ima#e


28/61

( )

( ) (3

(3

"

(3

"

"

" "

" "

%%

V V m

C A

C A −=−−

−

−−−=

−−

=∴

3

7

3(

" " " x −=

+−=

" " −=

( )

( ) 47

3

7

3

7

"

" "

" "

" %

" %V −=

−−−

−

−

=−

=

( )

( ) 4

3

(3

7

(4

7

−=−−

−

−−−

=−−

=∴ "

"

" "

%%

V V M

C A

C A

ONPTBA) PONT8

• t a hole is fo*med at the ce"te* of mi**o*, the ima#e positio" a"d sie +ill "ot cha"#e.The i"te"sit' +ill *ed&ce depe"di"# o" the sie of the hole.• ;o* all o/


29/61

( ) R RV −=

−+

(

(

11

1

R RV (

4

(

11

1

−=

RV (

31

1

−=

3

1

(

3

(

3

(1

1

−=

−

−=⇒−

R

R

m R

V .

⇒ o/


30/61

%

V m −=

#0(

1

−−= V

$o*% cmV 30+=

#0

1

30

1

#0

1111=+−=+=∴

$% "

cm " #0+=∴

" seco"d case

3100

3

1 %V

%

V m −=−==

As " $%

111 =+

#0

131=−

%%cm% 1(0−=

D: % T+o o/


31/61

V " %

111 −=∴

14

1

3"

1

10

1−=+−=

cm% 14−=∴

ista"ce of the o/


32/61

( ) " % 1−−= η

D: 4% A" o/


33/61

of c&*(at&*e is 1!cm. f the /e"d is 2!cm f*om the pole of the mi**o*, the" the *atio of the

le"#ths of the ima#es of the &p*i#ht a"d ho*io"tal po*tio"s of the +i*e is

8ol&tio": cm R

" "(

10

(===

;o* pa*t PD

01 '% "

" '

−

=

( ) 3(0"" 0

0

' ' −=×

−−−

−=

;o* pa*t DR

0

(

( '% "

" '

−

=

( ) '(0"" 0

0

(

' ' =×

−−−

−=

1

3

(

1 =∴ '

'

• ONPT O; NTON8 ;ORMB)A $;OR A MRROR%" this fo*m&la, the o/


34/61

i(idi"# e0&atio" $1% a"d $2% 'ields

I!

O!

IM

OM

IC

OC == $si"ce M is close to P%

$o*% y "

" x

y "

" x

++

=−−

y " " y x " x y " y x " " x −+−=−+− ((

$o*%( " y x =

y x " =∴

1% As(

" y x = $o*% y

x 1α

$i.e.% The dista"ce of o/


35/61

This is the e0&atio" of a *ecta"#&la* h'pe*/ola +ith its o*i#i" shifted to ( ) " " , a"d x /ei"#al+a's "e#ati(e +hile ' lies /et+ee" O a"d f . $see fi#&*e% fo* a co"ca(e mi**o*, & is al+a's

"e#ati(e, v ca" /e positi(e $o*% "e#ati(e, H f is "e#ati(e

" " and y$ x% −===∴ ,

e ha(e, fo*m

( ) ( ) ( " " $ " % =−−( ) ( ) ( " " y " % =++

O* ( )[ ] ( )[ ] ( " " y " x =−−−−

(ide"tl' it is a#ai" a" e0&atio" of a *ecta"#&la* h'pe*/ola +ith o*i#i" of coo*di"ates shifted tothe poi"t $f, f% $see fi#&*e↓%

3% -RAP@ O;$

1 ?R8B8

%

1

;*om mi**o* fo*m&la

" %$

111=+

P&tti"# x%=

1 a"d y

$=

1, +e ha(e

y y x 1=+

t is the e0&atio" of a st*ai#ht li"e ha(i"# a slope G1 $o*% 1 acco*di"# as u a"d v /ea* the same

$o*% opposite si#"s. The i"te*cepts o" a"d ' ais a*e each ( ) "

or "

11 −+ acco*di"# as the

o/


36/61

;o* a co"ca(e mi**o*:

u is al+a's F(e

v ca" /e positi(e $o*% "e#ati(e a"d f is F(e.

;o* a co"(e mi**o* u is al+a's "e#ati(e v is al+a's positi(e a"d f is al+a's positi(e.

• ONPT O; RT)A AN-)he" a *a' of li#ht is t*a(eli"# fo*m de"se* medi&m to *a*e* medi&m, it #et *ef*acted a"d the

*a' de*i(ates a+a' fo*m the "o*mal.

f +e =eep i"c*easi"# a"#le of i"cide"ce the" at a" a"#le, the a"#le of *ef*actio" /ecomes 9!! .This is ="o+" as *itical FA"#le $c%.

he" a"#le of i"cide"ce is i"c*eased, f&*the* the *a' #ets *eflected /ac= i" the same medi&m.

This phe"ome"a is ="o+" as T..R.

Acco*di"# to 8"ells )a+

r

ia

b

si/

si/= µ

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 3#




37/61

0'0si/

si/ C a

b i= µ

C a

b isi/= µ

=

C

ab

isi/

1 µ

⇒ depe"ds o" colo&* a"d a"d temp

⇒ Red K (iolet ∴Red L (iolet

⇒ f temp ↑C D: 1% The s&m $diamete* d% s&/te"ds a" a"#le *adi&s at the pole of a co"ca(e mi**o* of focal

le"#th f. ;i"d te diamete* of the ima#e of s&" fo*med /' mi**o*E

8ol&tio": " %$

111=+ +e #et

" $ −= 11 $ u is (e*' la*#e so 0

1≈

%

O* " $ −=

t mea"s ima#e is fo*med at foc&s

Ta=i"# ,, " as *adi&s a"d &si"#

" r and d (henr

===

θ

" d or " d θ θ ==∴

• R;RATON AT 8P@RA) 8BR;A:

;*om s#e∆ O a"d





38/61

e ha(e β α +=i

A"d ( ) r r or r r −=+= β β ;*om 8"ells la+

r

i

si/

si/

1

( = µ

µ

r i si/si/ (1 µ µ =;o* small a"#le of i"cide"ce , +e ca" +*ite r r and ii ≈≈ si/si/

r i (1 µ µ =∴ [ ] [ ]r −=+ β µ β α µ (1As Hi is small, a"d so r and β α , a*e also small. Th&s

( ) β α β α ta/ta/ +=+

R

h

%

h

++

−=

A"d ( )V

h

R

hr −=−β

−=

++

−∴

$

h

R

h

R

h

%

h(1

µ µ

Afte* simplif'i"# +e #et

R%$1(1( µ µ µ µ −=−

R$

11

1

(

1

( −=− µ µ

µ

µ

µ

→−=− R%$

11(

1

(

1 µ µ This fo*m&la is de*i(ed fo* co"(e s&*face a"d fo* *eal

ma#e;*om de"se* to *a*e* medi&m

R%$(1(1 µ µ µ µ −=−

D: @o+ ca" +e de*i(e a mathematical ep*essio" fo* the e0&atio" of a *a' i" the medi&mE The

medi&m is of (a*ia/le *ef*acti(e i"de. Ra' of li#ht is i"cide"t at a" a"#le α at ai* medi&mi"te*faceE

A"al'sis: @e*e t+o cases a *ise. Ref*acti(e i"de is (a*'i"# eithe* as f&"ctio" of ' $o*% f&"ctio"

of .

ase: ( ) ( )..ei y " = µ Ref*acti(e i"de (a*ies +ith '

At some hei#ht h a"#le of i"cide"ce is yθ

a"d *ef*acti(e i"de is( ) y "

f*om 8"ells )a+





39/61

=θ µ si/ co"sta"t( ) y y " θ α si/si/1 =×∴ >>..$1%

8lope of c&*(e at A

( ) ydx

dyθ −= '0ta/

dx

dy y =⇒ θ cot

;*om e0&atio" $1%

( ){ }α

α

si/

si/(( −

= y "

dx

dy

ase: ( ) ( )..ei y " = µ Ref*acti(e i"de (a*ies as f&"ctio" of x. Acco*di"# to 8"ells )a+

=θ µ si/ co"sta"t;o* i"itial *ef*actio" at the ai* medi&m i"te*face

( )00

'0si/si/1 θ µ α −=×( )

00 '0si/si/ θ µ α −=

00 cossi/ θ µ α =∴

@e*e 0θ a"#le of *ef*acti"# *a' at poi"t A +ith O

8o0

0

si/cos

µ

α θ =

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 3'




40/61

A"d (0

(

0

si/1si/

µ

α θ

−=

No+ 8"ells )a+ at M #i(es( ) 00 si/si/ θ µ θ = x x "

O*( ) (

0

(

0 si/1si/

µ

α µ θ −=

x " x

( ) x " xα µ

θ ((

0 si/si/

−=∴

No+ slope of ta"#e"t at M is #i(e" as

xdx

dyθ ta/=

( ){ } α µ

α µ ((

0

(

((

0

si/

si/

+−

−=

x " dx

dy

D: 1% f y+= 1 µ a"d *a' of li#ht is i"cide"t at #*ai"# i"cide"ce at o*i#i", the" fi"d e0&atio" of

path of *ef*acted *a'.8ol&tio": e ca" &se *es&lt de*i(ed a/o(e fo* +hich

( ) 0'01 =+= α and y y " (1

ydx

dy =∴

8o4

( x y =

D: 2% A" o/


41/61

(3( = µ

R C 1!cmcmV 1"0=∴

∴The *a's a*e co"(e*#i"# /e'o"d of at 1!cm fo*m D. A#ai" *ef*actio" ta=es place atthe pla"e s&*face.

;o* *ef*actio" at seco"d face

1".1,1(

==∞= µ µ Rcm140+= µ

5=$

Bsi"# R%$

(1(1 µ µ µ µ −=−

∞−=

+− ".11

140

".11

$

3.'3=$∴The *a' meet ais at 93.3cm fo*m poi"t D.

• PRO)M8 ON R;RATON1% A li#ht *a' is i"cide"t at a" a"#le of i"cide"ce do&/le that of *ef*actio" o" o"e face of a pa*allel

sided t*a"spa*e"t sla/ of *ef*acti(e i"de ,, µ a"d thic="ess Ht. ;i"d thelate*al displaceme"t of the *a'E

8ol&tio": r i (=

( ) ( )r t

r

r t

r

r r t

r

r it D ta/

cos

si/

cos

(si/

cos

si/==

−=

−=

Asr

i

si/

si/= µ

r

r r

r

r

si/

cos.si/(

si/

(si/ == µ

r cos(= µ

(cos

µ µ =

1(

ta/

(

−

=∴

µ r

1(

(

−

=∴

µ t D

µ

µ (4−=∴ t

D





42/61

D: 2% A li#ht *a' is i"cide"t o" a t*a"spa*e"t sla/ of R. . (= µ , at a" a"#le of i"cide"ce 4π . ;i"d

the *atio of the late*al displaceme"t s&ffe*ed /' the li#ht *a' to the maim&m (al&e +hich it

co&ld ha(e s&ffe*edE

8ol&tio": (,4

== µ π

i

#(si/

4si/

si/

si/π

π µ =∴=⇒= r

r r

i

( )

#cos

#4si/

cos

si/

π

π π

−

=−

=t

r

r it D

−=

#ta/.

4cos

4si/

π π π t

×−=

3

1

(

1

(

1t

( )13#

−= t

D ( )

#

#(3 −=∴

t

D

D: 3% )i#ht of a ce*tai" colo&* has 2!!! +a(es i" o"e millimete* of ai*. ;i"d the "&m/e* of +a(es of

that li#ht i" o"e millimete* le"#th of +ate* a"d #lass *especti(el'E

8ol&tio": =aλ +a(ele"#th i" ai*=mλ +a(ele"#th i" medi&m

The "&m/e* of +a(es of that li#ht i" a le"#th of Hd +ill /e

a

d n

λ =

1

A"dm

d n

λ =(

m

m

a

nn µ

λ λ ==∴

1

(

1( nn m ×=∴ µ

(##0(00033.1( =×=n i" +ate*3000(000"0.1( =×=n i" #lass

D: % )i#ht f*om a sodi&mlamp ( )nm"=λ t*a(e*ses a dista"ce of 6!m i" a chlo*ofo*m ( )4".1= µ i" a ce*tai" time. ete*mi"e the time diffe*e"ce occ&**i"# +he" li#ht happe"s to t*a(e*se the

same le"#th i" eth'l ethe* ( )3".1= µ

8ol&tio":mc

d t = ( )

sm

mt ch#oro"orm 103

4".1#0

1 ×=

;o* eth'l ethe*

( ) sm

mt r e

103

3".1#0. ( ×

=

(1 t t t −=∆

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 4(




43/61

( )30.14".11030

#0

−×

= m

sec100.( −×=

D: 5% A *ecta"#&la* #lass sla/ of thic="ess 12cm is placed o(e* a small coi" =ept o" a ta/le. A thi"

t*a"spa*e"t /ea=e* filled +ith +a#e* to a hei#ht 6cm placed o(e* the /loc=. ;i"d the

appa*e"t shift of the positio" of the coi", +he" (ie+ed f*om a poi"t di*ectl' a/o(e itE

8ol&tio":

−=

1

11

11

µ t S

−=

3

(11(

cm4=

−=

(

((

11

µ t S

−=

4

31#

C 1.5 cm

cmS S S "."".14(1 =+=+=∴

D: 6% The time ta=e" /' li#ht to co(e* a dista"ce of 9mm i" +ate* isIIII

8ol&tio": smC ( 104

'

34

103

×=×=

sec10410'

410' 11

3

−−

×=×

××

== (C d

t

ns'11 10104 ××= −

ns04.0=





44/61

D: 7% A *a' i"cide"t at a" a"#le of i"cide"t 6!! e"te*s a #lass F sphe*e of R. 3= µ . The *a' is

*eflected a"d *eflected a"d *ef*acted at the fa*the* s&*face of the sphe*e. The a"#le /et+ee"

*eflected a"d *ef*acted *a's at this s&*face isIIIII

8ol&tio":r

i

si/

si/= µ

(1

3

(

3

#0si/si/

0

=== µ

r

030=∴r

P C D 030=∠=∠=∠∴ r !)C C!)

A"#le /et+ee" *eflected *a' DR a"d *ef*acted *a' D8 at the othe* face0

#010 −−= r 000

'0#03010 =−−=

• R;RATON AT 8PRA) 8BR;A8D: 1% 8&"shi"e *eco*de* #lo/e of 3!cm diamete* is made of #lass of *ef*acti(e i"de ".1= µ . A *a'

e"te*s the #lo/e pa*allel to the ais. ;i"d the positio" f*om the ce"t*e of the sphe*e +he*e the

*a' c*osses the p*i"cipal aisE

8ol&tio":

;o* fi*st *ef*actio" $Ra*es to de&ces%

".1( =−∞= µ %

cm R 1"11 +== µ

R$

1(1(

(

µ µ µ µ −=−∴





45/61

% RV

11(( µ µ µ µ +

−=

( ) 3011

1"

1".1".1=

∞−+

−=

V

cmV 4"=

;o* seco"d *ef*actio" $do&ses to *a*e*%( ) cm%cm R 1"304",1" =−=−=

Bsi"# R%V

(1(1

µ µ µ µ −=−

( ) cmV or V

".74

30

30

1

1"

".11

1"

".1

1===

−−

=−

∴ista"ce of ima#e f*om ce"t*e of #lo/e is $15 G 7.5% C 22.5cm

D: 2% A pa*ticle eec&tes a simple ha*mo"ic motio" of amplit&de 1.!cm alo"# the p*i"cipal ais of a

co"(e le"s of focal le"#th 12cm. The mea" positio" of oscillatio" is at 2!cm f*om the le"s. ;i"d

the amplit&de of oscillatio" of the ima#e of the pa*ticleE

8ol&tio": he" the pa*ticle is

At R

cm% 1'−=51 =V cm " 1(=

+==−

% " V " %V

111111

1

1'1(

7

1'

1

1(

11

1 ×

=−=V

7

1'1(1

×=V

he" the pa*ticle is at left et*eme positio"

cm " V cm% 1(5,(1 ( ==−= ( )

(11(

'

(1

1

1(

1111111

(( ×

=−=+==−% " V

or " %V

∴Amplit&de of oscillatio" of ima#e(

(1 V V −

=

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". 4"




46/61

cm

×−

×=

'

(1(

7

1'1(

(

1

cm("7.(=

D: 3% A poi"t o/


47/61

8ol&tio": ma#e fo*med /' fi*st le"s

( )10

1

30

11111

1111

=−

−=−V

or " %V

( ) cmV or V

1"10

1

30

111

1

==+

The ima#e fo*med /' the fi*st le"s se*(e* as the o/


48/61

cm R

" 40".0

(0

1".1

(0

11

(

1 −=−

=−

−=

−−

= µ

;o* seco"d pla"o co"ca(e le"s

cm R

" #0".0

30

1".1

30

11

(

( −=−=

−−=

−−

= µ

The focal le"#th of the li0&id le"s is #i(e" /'

( )

+−=

(1

(

3

1111 R R "

µ

R 1 C 2!cm, R 2 C 3!cm ("( = µ cm " 3 =∴

cm " " " " 1(

1

1

#0

1

40

11111

3(1

=+−−=++=∴

cm " 1(=∴

D: 6% -i(e" the o/


49/61

D: 4% A *a' of li#ht passes th*oh a medi&m +hose *ef*acti(e i"de (a*ies +ith dista"ce as

+=

a

x10 µ µ . f the *a' e"te*s the medi&m pa*allel to the ais, +hat +ill /e the t*a


50/61

8ol&tio": " b " b V V V −−=

" b V V +=1#

V

V b=∴ µ

41# += bV V

1(

3

4 =

1(=bV scmV '1(4

3 =×=

D: 1!% 8ola* *a's a*e i"cide"t at 5! o" the s&*face of +ate* ( )34= µ . hat is the le"#th of theshado+ of a pole of le"#th 1.2m e*ected at the /ottom of the po"d, if the pole is (e*tical

ass&mi"# that !.2m of the pole is a/o(e the +ate* s&*faceE

8ol&tio": Appl'i"# 8"ells la+ at poi"t c

θ si/3

44"si/1

0 =×

(4

3

si/ =θ

@e*e mCD AE (.0==

BE BE

CE

BC ===1

ta/θ

( )(1si/

BE

BE

+=θ

( )(1(4

3

BE

BE

+=

m BE #(".0=∴ The le"#th of shado+ C A C A G C !.2G!.625 C !.425

D: 11% " a la=e, a fish *isi"# (e*ticall' to the s&*face of +ate* &"ifo*ml' at the *ate of 3ms, o/se*(es a/i*d di(i"# (e*ticall' to+a*ds the +ate* at a *ate of 9ms (e*ticall' a/o(e it. The act&al (elocit'

of the di(e of the /i*d isIIIIIII ( )34= µ 8ol&tio":

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". "0




51/61

D R

D A

.

.= µ

y

y = µ

y y µ =∴ ,

, y xh +=∴

y xh µ +=iffe*e"tiati"#

dt

dy

dt

dx

dt

dh µ +=

dt

dy µ +=3'

( ) sm

t d

yd ".4

34

#==

D: 12% A co"(e le"s of focal le"#th !.2m is c&t i"to t+o hal(es each of +hich is displaced /' !.!!!5m

a"d a poi"t o/


52/61

m$ #.0=

D: 13% A pole 5m hi#h is sit&ated o" a ho*io"tal s&*face. 8&" *a's a*e i"cide"t at a" a"#le 3!! +ith the

(e*tical. The sie of shado+ i" ho*io"tal s&*face isIIIIII

8ol&tio":

"30ta/ 0 BC =

m BC 3

"30ta/"

0 ==

D: 1% The 8&" s&/te"ds a" a"#le 0".0=α at the pole of a co"ca(e mi**o*. The *adi&s is c&*(at&*e ofco"ca(e mi**o* is R C 1.5m. The sie of ima#e fo*med /' the co"ca(e mi**o* isIIIII

8ol&tio": As 8&" is at i"fi"it' ima#e is fo*med at the foc&s of mi**o*

1% 10".0(

1 0 ××=

10"10

".0(

1×××=

π

C !.65 cm

%

D !O) S ==∠ α O*

=S

i

D

Dma#"ificatio"

%

"

%

$==

%

R

D

D

S

i

(=

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". "(




53/61

S i D%

R D ×=

(

• MA-N;AOTN N A8 O; BR? 8BR;A:o"side* a" ete"ded o/


54/61

• R;RATON AT PR8MA p*ism is a po*tio" of a t*a"spa*e"t medi&m /o&"ded /' t+o pla"e faces i"cli"ed to each

othe* at a s&ita/le a"#le.

a% alc&latio" of a"#le of e*i(atio":

" passi"# th*oh the p*ism, *a' Q) s&ffe*s t+o *ef*actio"s a"d has t+eed th*oh a"δ = ')!N . $+ith is a"#le of di*ectio"%

" !'M ∆ , !M' !'M ∠+∠=δ

( ) ( )((11

r ir i −+−=δ ( ) ( )

(1(1 r r ii +−+=δ >>>>>$1%

" O'M ∆ 0(1 10=++∠ r r O >>>>>$2%

" D&ad*ilate*al A)OM,

As 010=∠+∠ M ' $∴8&m of a"#les of a D&ad C 36!%010=∠+∴ O A

∴&si"# e0&atio" $2% +e ca" +*iteO Ar r O ∠+++∠

(1

Ar r =+ (1 >>>>>.$3%

P&tti"# $3% i" $1%

( ) Aii −+= (1δ >>>>>$% $fo* /i##e* *ef*acti"# a"#les%

f,,

is the *ef*acti(e i"de of the mate*ial of the p*ism, the" acco*di"# to 8"ells )a+

1

1

1

1

si/

si/

r

i

r

i== µ $+he" a"#les a*e small%

11 r i µ −∴ simila*l' (( r i µ =

P&tti"# the a/o(e t+o i" e0&atio" $% +e #et

( ) Ar %r % −+= (1

δ

( ) Ar r −+= (1

µ δ

( ) A1−=∴ µ δ $+he" *ef*acti"# a"#le a*e small%This is the a"#le th*oh +hich a *a' de*i(ate o" passi"# th*oh a thi" p*ism of small

*ef*acti"# a"#le A.

P*ism fo*m&la:

" mi"im&m de*i(atio" positio"

i1 C i2 C i a"d *1 C *2 C *

∴ f*om e0&atio" $3%





55/61

Ar r =+ Ar =(

A"d f*om e0&atio" $%

( ) Aiim −+=δ Ai

m −=(δ

( )(

( mm A

ior i A δ

δ +

==+∴

∴ f*om 8"ells )a+

( )(si/(

si/

si/

si/

A

A

r

imδ

µ

+

==

Note : The de(iatio" th*oh a p*ism is maim&m +he" i1 C 9!!.

Th&s Aim −+= ('0δ

• MAMBM ?ATON:

;o*0

1 '0=i

5( =∴ i

At s&*face

111 si/.si/ r i µ µ =

1

0si/.'0si/1 r µ =×

=∴

µ

1si/

1r

( )C r or r θ µ =

=

−

1

1

1

1si/

e ="o+ that Ar r =+ (1 ( )1( r Ar −= ( )C Ar θ −=(

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". ""




56/61

;o* s&*face

(( si/si/ ir = µ

( )C Ai θ µ −= si/si/ (( )[ ]θ µ −= − Ai si/si/ 1

(

ONPT: 8ometimes a pa*t of a p*ism is #i(e" a"d the =eep o" thi"=i"# +hethe* ho+ sho&ld

+e p*oceedE To sol(e s&ch p*o/lems fi*st complete the p*ism the" sol(e as the p*o/lems of

p*ism a*e sol(ed

efects i" ma#e fo*med /' le&ses:

The defect i" the le"s o" acco&"t of +hich it does "ot fo*m a +hite poi"t ima#e of +hite poi"t

o/


57/61

;o* a p*ism of small *ef*acti"# a"#le of de(iatio" is

A"#&la* dispe*sio": t is the a"#le i" +hich all colo&s of +hite li#ht a*e co"tai"ed

d( C de(iatio" of (iolet colo&*

d* C de(iatio" of *ed colo&*( )∴θ A"#&la* dispe*sio" C d( d*As ( ) Ad V V 1−= µ

( ) Ad V S 1−= µ ( ) ( ) A Ad d r V r V 11 −−−=−∴ µ µ

( ) A

r V 11

+−−= µ µ

( ) Ad d r V r V µ µ −=−ispe*si(e Po+e* $+%: Ratio of a"#&la* de(iatio" to the mea" positio" p*od&ced /' the p*ism.

( )

( ) ( )11 −=

−−

=−

= µ

µ

µ

µ µ ω

d

d

d d r $r $

Note: 8i"#le p*ism p*od&ces /oth de(iatio" a"d dispe*sio" sim&lta"eo&sl'. t ca""ot #i(e de(iatio"

+itho&t dispe*sio" $o*% dispe*sio" +itho&t de(iatio". @o+e(e* a s&ita/le com/i"atio" of t+o

p*isms ca" do so.

ispe*sio" of li#ht occ&*s /eca&se (elocit' of li#ht i" a mate*ial depe"ds &po" its colo&*

The*e is "o dispe*sio" of li#ht *ef*acted th*oh a *ecta"#&la* #lass sla/.

om/i"atio"s of p*im:

% e(iatio" +itho&t dispe*sio":

Net dispe*sio" C !, Net de(iatio" ≠ !Necessa*' co"ditio"

( ) ( ) 011 =−+− RV RV δ δ δ δ ( ) ( 0 =−+− A A RV RV µ µ µ µ

" this 8it&atio"





58/61

Net de(iatio" C ( ) ( ) ( ) ( )

−−

−−+−=−+−=+ +1

1111

RV

RV A A µ µ

µ µ µ µ µ µ δ δ

( ) ( ) ( )

( ) A A

RV

RV

11

µ µ

µ µ µ µ

−

−−−−=

( ) ( )

( )

( )

( )

−

−×

−

−−=

1

11

RV

RV A µ µ

µ

µ

µ µ µ

−

1

1 1

ω

ω δ

Bs&all' ω


59/61

8ol&tio": ( ) ( ) 00(41".11 =−=−= A &rism µ δ

mirror &rismtota# δ δ δ +=

( ) ( )i A (101 −+−= µ

( ) ( )00 ((1041".1 ×−+−=1717#(

00 =+=

D: 2% A co"tai"e* co"tai"s +ate* &pto a hei#ht of 2!cm a"d the*e is a poi"t so&*ce at the ce"t*e of the

/ottom of the co"tai"e*. A *&//e* *i"# of *adi&s H* floats ce"t*all' o" the +ate*. The ceili"# of

the f*om is 2.!m a/o(e the +a#e* s&*face.

$a% ;i"d the *adi&s of the shado+ of the *i"# fo*med o" the ceili"# if * C 15cm.$/% ;i"d the maim&m (al&e of H* fo* +hich the shado+ of the *i"# is fo*med o" the ceili"#

( )34=( µ 58ol&tio": a% Bsi"# 8"ells )a+

r i si/si/ = µ

(((((00

1(01"

1"

3

4

+×=

+×

x

x

cm x3

00=∴

∴ Radi&s of shado+ C3

001" +

cm3

4"=

m1.(=

/% ;o* shado+ to /e fo*med a"#le of i"cide"ce sho&ld /e less tha" c*itical a"#le

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". "'




60/61

&si"# 8"ells )a+

0

((

+a

+a '0si/1(03

4×=

+r V r

((

+a

(

+a (0''1# ×+= r r ((

+a (0'7 ×=r

mcmr ((#.0(0

7

'

+a =×=D: 3% Mo"och*omatic li#ht falls o" a *i#ht a"#led p*ism at a" a"#le of i"cide"ce 5!. The eme*#e"t

li#ht is fo&"d to slide alo"# the face A. ;i"d the *ef*acti(e i"de of mate*ial of p*ismE

8ol&tio":

C r θ =( >>>..$1%0

(1 '0==+ Ar r

1( '0 r r −= >>>..$2%

1'0 r C −=∴θ

( )1

'0si/si/ r C

−=θ

1cossi/ r C =θ

1cos

1r =

µ a"d (1

(

1

11cos1si/

µ −=−= r r

8"ells la+ AR

10 si/4"si/1 r µ −

(

0 114"si/

µ µ −=

1(

1 ( −= µ

1(

1 ( −= µ

".1(

3( == µ

".1= µ

Flat No.301, Rukkus & Yellus Arcade, Fever Hospital Road, Barkathpura, Hd!"000#". #0




61/61

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