DEPARTMENT OF CIVIL ENGINEERING 
Program: B. Sc in Civil Engineering

Course Title:

Mechanics, Heat, Thermodynamics, Waves, Oscillations and Physical Optics- Lab

Course code:        PHY 103

Assignment

Experiment No-01                                   Experiment Done Date: 28.01.2015

Name of the Experiment:

To determine the focal length and hence the power of a convex lens by displacement method with the help of an optical bench.

Submitted by:

Name: Mohammed Abdur Razzak

Roll No:  3326,  Registration No: WUB/10/13/60/3326, 

Batch No: 60/C, Semester No: Fourth, Year: Second.

Submitted To:

Name:  Md. Shohel Rana

 Designation:  Lecturer in physics, Basic science Division (WUB)                 Date of Submission:

Experiment No.:04

Experiment Name: Determine the focal length and hence the power of a convex lens by displacement method with the help of an optical bench.

Theory: If the object and the image screen be so placed on an optical bench that the distance between them is greater than four times the focal length (f) of a given convex lens, then there will be two different positions of the lens which for which an equal sharp image will be obtained on the image screen.

                                                                                                                     

The fig represent respectively the positions of the object and the image screen and the two different positions of the lens for which an equally sharp image is obtained.

Let the distance Ol =D and L₁ – L₂ = x.

From the lens equation , we have

Or,   (since u + v =D)

Applying sign convention, u is negative.

Or,

Or, u² – ud =df = 0

Solving the above equation which is quartic, we have two values of u corresponding to the two positions of the lens. These are

u₁ =  -  position L₁ of the lens

And u₂ =  +  position L₂ of the lens

Then x = L₁  L₂ = u₁  u₂ =

Or   x² = D² – 4Df

Or   f =  ……………….. (1)

Where D is the distance between the object and the image and must be greater than 4f and x is the distance between two different positions of the lens.

The power P of the lens s as usual given by the relation,

P =  diopters

Results:

Table I

No. of obs.	Position of				Displacement of Lens X = L1 – L2 (cm)	Apparent distance between object and image D’ = O	Corrected distance between object and image D = D’ +
	Object (O)	Image (I)	Lens at
			L1	L2
1	0	45	16	28.2	12.20	45
2	0	50	14.4	34.4	20.00	50
3	0	55	14	40.30	26.30	55
4	0	60	12.4	46.00	33.60	60
5	0	65	12.1	51.00	38.90	65

Table II:

No. of obs.	Lens displacement (x) from Tab. II	Corrected Distance (d) from Tab. II	Focal length	Mean focal length (f) cm	Power P =
1	12.20	45	10.42	10.45	9.56
2	20.00	50	10.50
3	26.30	55	10.60
4	33.60	60	10.30
5	38.90	65	10.43

Hook's Law

Hooke's law:

Hooke's law: the force is proportional to the extension

Manometers are based on Hooke's law. The force created by gas pressure inside the coiled metal tube at right unwinds it by an amount proportional to the pressure.

The balance wheel at the core of many mechanical clocks and watches depends on Hooke's law. Since the torque generated by the coiled spring is proportional to the angle turned by the wheel, its oscillations have a nearly constant period.

Hooke's law is a principle of physics that states that the force  needed to extend or compress a spring by some distance  is proportional to that distance. That is: where  is a constant factor characteristic of the spring, its stiffness. The law is named after 17th century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram.^[1][2] He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force").

Hooke's equation in fact holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, a musician plucking a string of a guitar, or the filling of a party balloon. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean.

Hooke's law is only a first order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. In fact, many materials will noticeably deviate from Hooke's law well before those elastic limits are reached.

On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. For this reason, Hooke's law is extensively used in all branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock.

The modern theory of elasticity generalizes Hooke's law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the "proportionality factor" may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.