Physics Project

PHYSICS PROJECT

PHYSICS PROJECT

On

On

Determ

Determinat

ination Of 

ion Of 

refractive index of 

refractive index of 

Different Liquid using a

Different Liquid using a

o!!o" #rism$

o!!o" #rism$

PROJECT PREP%RED &Y'

PROJECT PREP%RED &Y'

(RID)L &H%SI*+II &

(RID)L &H%SI*+II &

Session ' ,-./0,-.1

Session ' ,-./0,-.1

&oard2s Ro!! *um3er '

&oard2s Ro!! *um3er '

Ha##4 (ode! Scoo!

Ha##4 (ode! Scoo!

CERTI5IC%TE

CERTI5IC%TE

Tis is

Tis is ere34 to certif4

ere34 to certif4 tat6 te orig

tat6 te origina!

ina!

and genuine investigation "or7 as 3een

and genuine investigation "or7 as 3een

carried out to investigate a3out te

carried out to investigate a3out te

su38ect matter and te re!ated data

su38ect matter and te re!ated data

co!!ection and investigation as 3een

co!!ection and investigation as 3een

com#!eted so!e!46 sincere!4 and

com#!eted so!e!46 sincere!4 and

satisfa

satisfactori!4 34 (RID)L of

ctori!4 34 (RID)L of CL%SS +II &6

CL%SS +II &6

Ha##4 (ode! Sc

Ha##4 (ode! Scoo! 6 re

oo! 6 regarding is

garding is

#ro8ect tit!ed

#ro8ect tit!ed

9Determination Of

9Determination Of refractive inde

refractive index of

x of

Different Liquid using a o!!o" #rism:$

Different Liquid using a o!!o" #rism:$

Teacer2s Signature

Teacer2s Signature

%C;*O<LED=E(E*T

It "ou!d 3e m4 utmost #!easure to ex#ress

m4 sincere tan7s to (4 P4sics Teacer

(rs$(I*%;SHI in #roviding a e!#ing and

in tis #ro8ect$ Teir va!ua3!e guidance6

su##ort and su#ervision a!! troug tis

#ro8ect tit!ed

9Determination Of

refractive index of Different Liquid

using a o!!o" #rism:

 are res#onsi3!e

for attaining its #resent form$

(RID)L

+II &

CO*TE*TS

S!$ *o

Item Page *o$

.$ O38ective ,$ Introduction >$ %##aratus ?$ Teor4 /$ Procedure 1$ O3servations @$ Diagrams A$ Ca!cu!ations B =ra#s $ Precautions .-$ &i3!iogra#4

O&JECTIES'



To stud4 te variation of te ang!e of   deviation "it te ang!e of incidence using Ho!!o" =!ass Prism and to determine te ang!e of minimum deviation$



To find out te refractive index of various !iquids using a Ho!!o" Prism$

I*TROD)CTIO*'

Tis #ro8ect is of Investigator4 T4#e$ In tis #ro8ect6 a o!!o" #rism as 3een used to ca!cu!ate te refractive index of various !iquids$ Te o!!o" #rism is fi!!ed "it !iquid and ten te ex#eriment is #erformed$

%PP%R%T)S'

 Dra"ing &oard  Seet of Pa#er   Ho!!o" =!ass Prism  =ra# Pa#er 

 Protractor   Dra"ing Pins

 %!! Pins  Penci!

THEORY'

Refraction '

In a omogenous medium6 !igt trave!s a!ong a straigt !ine6 3ut "enever it fa!!s on a surface of  anoter medium6 a ver4 sma!! fraction of it is ref!ected 3ac7 and most of te !igt #asses into te medium6 toug "it a cange of direction$ Tis #enomenon of te 3ending of !igt at te surface of  se#aration of te t"o medium is ca!!ed refraction of  !igt$

Causes of refraction

Tis #enomenon of refraction ta7es #!ace "en a 3eam of !igt enters a medium in "ic !igt enters a medium in "ic !igt trave!s "it a different ve!ocit4$

La"s Of Refraction

.$ Te incident ra46 te refracted and te norma! to te surface at te #oint of incidence !ie on te same #!ane$

,$ 5or an4 t"o given media6 te ratio of te sine of  te ang!e of incidence to te ang!e of refraction is a constant6 "ere it is te ang!e of incidence and is te ang!e of refraction$

(edium'

Te surrounding su3stance troug "ic te !igt trave!s$

 5or a monocromatic !igt6 te ratio of te sine of  te ang!e of incidence to te sine of ang!e of  refraction is a constant for an4 t"o given media$ If  I2 is te ang!e of incidence6 and r2 is te ang!e of  refraction6 tenF

SineG I

00000000000000000000000000000000000000  Constant SineG R

te constant is ca!!ed te refractive index$

5or most #ur#oses it ma4 3e assumed tat te refractive index is "it res#ect to air$ <en !igt trave!s from a rarer to a denser medium6 it 3ends to"ards te norma! and vice versa "en it goes from a denser to a rarer medium$ It as 3een ex#erimenta!!4 so"n tat

e!ocit4 of !igt in air  Refractive index of su3stance  000000000000000000000000000000000000

Refraction Troug Prism'

% trans#arent medium 3ounded 34 t"o #!ane surface inc!ined to eac oter at an ang!e is ca!!ed a Prism$ Te ang!e 3et"een te t"o faces is 7no"n as te ang!e of te #rism$

%ng!e of deviation

' Te ang!e troug "ic te incident ra4 of !igt is deviated is ca!!ed te ang!e of  deviation$ In fact it is te ang!e 3et"een te emergent ra4 and te incident ra4 #roduced$

%ng!e of minimum deviation

' %s te va!ue of te ang!e of incidence G. increases6 te ang!e of  deviation decreases ti!! for a #articu!ar va!ue of te ang!e of incidence6 it attains a minimum va!ue m 6 is ca!!ed te ang!e of minimum deviation$

Critica! ang!e

 '

It is tat ang!e of incidence in te denser medium for  "ic corres#onding ang!e of refraction in te rarer  medium is - degree$

.  u  00000000000000000000 Sin C <ere6 u 0 Refractive Index C0 Critica! ang!e

Te four #arameters on "ic ang!e of deviation de#ends are'

.$ %ng!e of #rism

,$ (ateria! of #rism

>$ %ng!e of incidence

Refraction troug Prism '

Teor4 on refraction troug Prism '

<en a ra4 of !igt #asses from one medium into te oter6 it eiter 3ends to"ards te norma! or a"a4 from te norma! in te second medium6 de#ending u#on "eter te second medium is denser or rarer "it res#ect to first medium$ Tis #enomenon is 7no"n as te Refraction of !igt

5or a #articu!ar #air of t"o media6 and for a #articu!ar "ave!engt of !igt Gco!our te ratio of  te sine of te ang!e of incidence and te sine of te ang!e of refraction is a constant quantit4 ca!!ed te Refractive Index of te second medium "it res#ect to te first medium$ It is re#resented 34'

Sin i

u  00000000000000000 Sin r 

Terefore6 te va!ue of te ang!e of incidence i can 3e o3tained in terms of te refracting ang!e % of te #rism and te ang!e of minimum deviation m and te

ang!e of refraction r can a!so 3e o3tained in terms of  te refracting ang!e % of te #rism$

Let %&C re#resent a section of te g!ass #rism and !et IP 3e a ra4 incident at ang!e i on te first face %& of te #rism at a #oint P$ *.P* is te norma!

to tis face$ Te materia! of te #rism is denser "it res#ect to air6 as suc te ra4 "i!! refract in te direction P ma7ing an ang!e r . "it te norma!

reacing te second face %C of te #rism at te #oint  ma7ing an ang!e r ,"it te norma! *,T$ Te

ra4 emerging in te direction E 3ending a"a4 from te norma! and ma7ing an ang!e e "it te norma!$

If te incident ra4 IP 3e #roduced 3ac7"ards to meet E #roduced at S6 te ang!e ;S is ca!!ed te ang!e of deviation is re#resented 34 D$ %ng!e &%C is ca!!ed te refracting ang!e of te #rism and re#resented 34 %$

To derive te re!ation'

% B D  i B e

In   SP6

 ;S or D is te externa! ang!e$ D   SP B  SP  i0r .B e0r ,  Gi B e 0 Gr . B r , $$$$$$$$$$$$$G. r . B r  , B  PT  .A- -r . B r ,  .A-- 0  PT $$$$$$$$$G, Ta7ing quadri!atera! %PT  %PT B  %T  -- B --  .A- - % B  PT  .A- - %  .A- 0  PT 0000000000000000G> 5rom G, and G> r . B r ,   %$$$$$$$$$$$G? 5rom G. and G?

 D  i B e 0  %

% B

 D  i B e

<en te ang!e of deviation D as minimum va!ue Dm te fo!!o"ing conditions are fu!fi!!ed'

i  e

and r . 0 r ,  r Gsa4

%##!4ing tese conditions in Eq$G, and G>

%  , r  % or r  00000 $$$$$$$$$$$G/ , and % B D m  , i %BDm Or i  000000000 $$$$$$$$$$$$G1

,

Sin i

Since u,  00000000

Sin _r 

<e o3tain on su3stituting te va!ue of Gi and Gr

  SinGi

since    000000000000

Sin Gr

SinG%BDmK,

  SinG%K,

Tus "e find tat "e can use te re!ation G@ for  determining te refractive index$ Te ex#eriment tus consists of finding of te va!ue of te refracting ang!e of minimum deviation Dm$ 5or finding te va!ue of Dm a curve is #!otted 3et"een te ang!es of 

incidenceG. and teir res#ective ang!es of deviation GD$

PROCED)RE'

.$ 5ix te seet of "ite #a#er on Dra"ing 3oard "it ce!!o ta#e or dra"ing #ins$

,$ Dra" a straigt0!ine +Y near!4 at te center of  te seet #ara!!e! to its !engt$ (ar7 #oints mar7ed as O at suita3!e s#acing on te !ine +Y and dra" norma! to te !ine +Y at #oint O$ Dra" straigt !ine P corres#onding to te incident ra4s tat are dra"n at te ang!es of incidence ranging from >- to 1- i$e$ for ang!es >/6?-6?/6/-6//  1- using a #rotractor$

>$ 5i!! te !iquid from o#en and of #rism$

?$ 5ix t"o #ins P and  a3out A cm on te incident ra4!ine and vie" its image "it one e4e c!osed from te side of &C of te #rism$ 5ix t"o #ins R and S on te #a#er suc tat te ti#s of tese #ins and te ti#s of tese images of te incident ra4 #ins6 a!! !ie on te same straigt !ine$

/$ Join te #oints Gi$e$ #in #ric7s S  R and #roduce it 3ac7"ards to meet te incident ra4 P #roduced$ Tus RS is te emergent ra4

corres#onding to te incident ra4 P$ Dra" arro" eads to so" te direction of ra4s$

1$ (easure te ang!e of deviation D "it Protractor$

@$ Re#eat at ste#s G? to A for different !iquids aving different va!ues of ang!e of incidence and measure te corres#onding ang!es of deviation D$ Ta7e at !east tree va!ues Gi from >-- to ?--$

A$ *o" #!ace te #rism on se#arate seet of  #a#er or on te same seet at a suita3!e #!ace and trace its triangu!ar 3oundar4 "it a sar# #enci!$ (easure te ang!e %6 of te triang!e so traced "it te e!# of #rotractor$

$ Record 4our o3servation in o3servation ta3!e$

P!otting of gra# 3et"een i  D$

P!ot a gra# 3et"een ang!e i and D for various sets of va!ues recorded in te o3servation ta3!e$

Precautions

.$ % sar# #enci! sou!d 3e used for dra"ing te 3oundar4 of te #rism$

,$ Te se#aration 3et"een te #ins sou!d not 3e !ess tan A cm$

>$ Te ang!e of incidence sou!d !ie 3et"een >-0?/$

?$ Te same and #rism sou!d 3e used for a!! o3servations$ So an in7 mar7 sou!d 3e #!aced on it to distinguis it as a refracting ang!e % of te #rism$

/$ Te #ins sou!d ave sar# ti#s and fixed vertica!!4 and te #in #ric7s sou!d 3e encirc!ed immediate!4 after te4 are removed$

1$ Pro#er arro" sou!d 3e dra"n to indicate te incident6 te refracted and te emergent ra4s$

@$ % smoot curve #assing #ractica!!4 troug a!! te #!otted #oints sou!d 3e dra"n$

O&SER%TIO*S

. 5OR H,O' S!$*o$ %*=LE O5 I*CIDE*C E %*=LE O5 DEI%TIO * .$ >/o ,/o ,$ ?-o ,?o >$ ?/o ,>o ?$ /-o ,/o /$ //o ,1o . 5OR SPIRIT' S!$*o$ %*=LE O5 I*CIDE*C E %*=LE O5 DEI%TIO * .$ >/o ,o ,$ ?-o ,1o >$ ?/o ,/o ?$ /-o ,@o /$ //o ,Ao

. 5or =!4cerin' S!$*o$ %*=LE O5 I*CIDE*C E %*=LE O5 DEI%TIO * .$ >/o >o ,$ ?-o >Ao >$ ?/o >/o ?$ /-o ?- o /$ //o ?.o ?$ 5OR &E*ME*E' S!$*o$ %*=LE O5 I*CIDE*C E %*=LE O5 DEI%TIO * .$ >/o ?-o ,$ ?-o >o >$ ?/o ?.o ?$ /-o ?, o /$ //o ?/o

C%LC)L%TIO*S

5ormu!a %##!ied'0 Sin G%BDm u  ,   00000000000000000000000 Sin G%K,

.$

<ater 

Sin G1-B,> ,  N u   SinG?.$/ 00000000000000000000000 0000000000000000000 SinG1-K, Sin >- -$11,1  .$>> -$/

,$

S#irit

Sin G1-B,/ , u _{ } SinG?,$/

00000000000000000000000 0000000000000000000 SinG1-K, Sin >- -$1@/1  .$>/  

-$/--->$

=!4cerin

Sin G1-B>/ , SinG?@$/ u _{ 000000000000000000000000000000000000000000000 0  0000000000000000000000000} SinG1-K, Sin >- -$@>@,  .$?@   000000000  -$/

?$

&enene

Sin G1-B>  u  ,  SinG?$/ 00000000000000000000000 0000000000000000000 SinG1-K, Sin >- .$/,

RES)LT

Gi Te ang!e of deviation D first decrease "it te increase in te ang!e o#0of incidence6 attains a minimum va!ue and ten increase "it furter  increase in ang!e of incidence$

Gii

Te refractive index of '0

i$ <ater  .$>> ii$ S#irit  .$>/ iii$ =!4cerine  .$?@