Optical lever.pdf

Optical Lever Method Experiments:

Determine the co-efficient of liner expansion of the given metal by optical lever method  Set-Up consists of: 1) 2) 3) 4) 5)

Pullinger’s appartus Optical liver Lamp(Laser) and Scale arrangement Meter Scale Stop Watch

Important

1. Please go through the lab manual / booklet before using any equipment. 2. Do not look at the laser beam directly. 3. Take proper protection during laboratory practice. 4. Do not remove any equipment or part of equipment from the experimental set-up without informing technical staff. 5. Do not forget to switch off the power supply of any instrument after using the instrument/s. 6. Write necessary information (if necessary) in the log book before leaving the laboratory. 7. Keep the experiment set-up clean before and after use. 8. Do not keep any extra items over the experimental table except the required instrument/s for the experiment. 9. Keep the tools in proper places after using them. 10. If you notice any item missing or found damaged in the lab, inform immediately to the technical staff. 11. Use of mobile phone is not allowed during the laboratory la boratory classes. 12. No 12.  No chairs, tables, stools etc. are a re to be taken out or brought bro ught inside the laboratory. 13. Food items are strictly prohibited inside the laboratory. 14. Keep the laboratory clean.

Aim Of The Experiment : To determine value of Co-efficient of linear expansion of a solid by optical liver method. Apparatus :

1. Pullinger’s appartus 2. Optical liver 3. Lamp(Laser) and Scale arrangement 4. Meter Scale 5. Stop Watch etc. Theory : Co-efficient of linear expansion of a material (α) can be determined using the relation

α=

l2 -l1 l1(t2-t1)

dp

x =

0 l (t -t ) /  C 1

2

1

=

0 /  C 2Dl (t -t ) 1

2

1

Where l1 = Initial length of the experimental rod  l2 = Final length of the experimental rod. t1 = Initial temperature of the rod  t2 =Final temperature of the rod  Again x = l2 – l1 =

 pd  2D

Where d = difference of initial and final vertical readings by which the light spot of the lamp and scale is   deflected. P = arm of the liver  D = distance between the mirror and the scale Description of Pullinger’s Apparatus: It consists of a steam jacket with inlet and outlet tubes for steam circulation. The whole system is fixed to a vertical wooden framework. There are holes at the top and   bottom of the jacket to introduce thermometers. The experimental rod is kept over a piece of plane glass  plate which is fixed to the frame. The top end of the experimental rod projects a little above a glass plate fixed to the top of the frame. One leg of the optical lever is placed to touch the centre of the projected top while the other two rests on the glass plate.

Optical Liver : It consists of a metallic frame resting on three legs. A plane mirror is fixed at right angle to the horizontal plane passing through the arm and parallel to the line joining two nearer legs( axis of lift of the mirror) F       >

M1

       d

E

      <

T >

> < <

B2

      >      x

2  

B1      < <  p D

M2

Q

> A AB1 = Initial position of the liver arm = p S AB2= Final position of the lever arm after a rotation  . B1B2 = x , ED = shift of the light spot on the scale = d  AS = Distance of the mirror from the scale =D T = Telescope The lever is place with its front leg touching the centre of the projected top of the experimental rod  and the other two legs resting on the glass plate. The expansion of the rod rotates the lever arm through an angle .

If x is the expansion of the rod then , in triangle AB1B2

x tan  =  p =>



Again in triangle FTQ tan 2 = 

2 =

 =

d 

2D d 

> ]

[ when  is very small then FT = FE and AS= D ] [ when  is very small then tan

D d 

x  p = 2D  pd   x= 2D 

d  FT FE = = TQ AS D

x =  p ——(i) [ when  is very small then tan

> ]

( by i )

Since the image rotates through an angle 2 when the mirror rotates through an angle . Procedures : 1. The length of the experimental rod is measured. The rod is placed in its proper place so that the  bottom end rests on the glass plate and the top end projects slightly above the top glass plate. 2. The lamp and scale is so arranged that the light spot reflection from the mirror becomes incident on the vertical scale. The reflected spot should be clear. Its cross-wire should be clear. 3. One thermometer is placed with its proper places. 4. The optical lever is placed with its mirror vertical and the front leg resting on the centre of the  projecting top of the experimental rod and the other two legs resting on the glass plate fixed to the top of the pullinger’s apparatus. The lamp and scale system should be place 1 meter away from the mirror. The scale reading 5. The rod is heated sending steamfrom the boiler. Temparature of the two thermometers are recorded at the interval of five minutes. 6. With rise of temparature, the position of the light spot changes. It goes up gradually. When temaparature becomes steady the spot also becomes steady. 7. The distance between the mirror and the scale is measured. 8. Length of the lever – arm is measured.

Table 1 (Reading for Length Expansion)` Sl.No Temparature ( 0C) 1

2

Position Of the Spot(cm) Shift of the spot(d=d1-d2)

Initial Temparature(t1) = (t1 + 273)K

d 1

Final Temparature(t2) = (t2+273) K 

d 2

Steady steady

d = d1 – d   2

Calculation:

Initial length of the rod (l 1) = ……… cm Length of the lever arm (P) = ……….cm Distance between the scale and the mirror (D) = ……… cm Shift due to the expansion (d) = ……… cm

dp

So, the co-efficient of linear expansion

α=

0 /  C 2Dl (t -t ) 1

2

1

Actual value of á = …………/ 0C Observed value = ………/ 0C

Actual value – Observed

P.C. of error

= Actual Value

 X 100%

= ………..%

Discussion : 1.The spot of Lamp and scale should be focused distinctly. 2.The optical lever should not be disturbed once it is placed in its position.No part of it should be touched before completion of the experiment. 3. Lamp and scale should be placed at a suitable distance so that the shift is sufficient. 4. Initial and Final readings of both the thermometers should be recorded.

Value of co-efficient of linear expansion for some material. Material

Co-efficient of linear expansion( α )

Copper

16.7 X 10-6/ 0 C

Aluminium

25.5 X 10-6/ 0 C

Brass

18.9 X 10-6/ 0 C

Iron(Cast)

10.2X 10-6/ 0 C

Iron(Wrought)

11.9 X 10-6/ 0 C

Note :  To find Value of co-efficient of linear expansion for some material following formula can be also used -

α=

Δl lΔ t

xd  where Δ l = x .θ = x . d  = 2D 2D and

Δ t = t2 - t1

[ x can be denoted by p and α can be denoted by M also]