1. newton’s rings -...

1

Department of Physics

R.B.V.R.R WMOEN’S COLLEGE (AUTONOMOUS) Name:

Roll No:

Date:

1. NEWTON’S RINGS

Aim: To determine the radius of curvature of a given lens by forming Newton’s Rings.

Apparatus: Plano convex lens, plane glass plate, microscope, sodium lamp.

Dm2 − Dn2

Formula: R = ------------- cm.

4λ(m−n)

Where,

R = radius of curvature of the plano convex lens

Dm = diameter of the mth ring.

Dn = diameter of the nth ring.

m, n = number of the chosen rings.

λ = wave length of light used (sodium lamp) = 5893 χ 10-8 cm or 5893 AO

Description & Theory:

Light from sodium lamp falls on a glass plate inclined at an angle 45° to the vertical.

Thus a parallel beam of light is reflected from the lower surface of the glass plate and falls on the

plano-convex lens at normal incidence, which is placed on another glass plate. Due to the air film

is formed between the glass plate and the Plano convex lens of large radius of curvature. The

parallel beam gets reflected from the top of the air film, shown as (1) in fig(2) and also from the

bottom of the air film shown as(2). These two beams are coherent and hence form interference

fringes which are observed directly through a travelling microscope. The rings are concentric

circles, with the common centre at the point of contact of the plano convex lens and the glass

plate.

Rays that are interfering to give

Newton’s rings 1 and 2

Fig(1). Fig(2).

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Procedure:

(1) Before starting the experiment, the glass plates and Plano convex lens should be

thoroughly cleaned.

(2) The centre of lens should be well illuminated by adjusting the inclination of glass plate at

45°. (3) Focus the eye piece of the traveling microscope on the cross-wire and move the

microscope in the vertical plane by means of rack and pinion arrangement till the rings

are quite distinct.

(4) The centre of the interference fringes should be dark but some times the centre appears

white. This is due to the presence of dust particles between glass plate and Plano-convex

lens. In this case the lens should be cleaned again.

(5) Move the microscope in a horizontal direction to one side of the fringes. Fix up the cross-

wire of the eyepiece tangential to the 21st dark ring and note this reading. Again the

microscope is moved in the horizontal plane and the cross-wire is fixed tangentially to the

successive dark fringes noting the vernier readings till the other side is reached. This is

shown in the fig (2).

Fig. (2)

Note the observations in the observation table shown.

Draw a graph with number of dark rings on the X-axis and the square of the diameter of the

rings on Y-axis. A straight line passing through the origin will be obtained. From the graph, the

values of Dm and Dn corresponding to mth and nth rings are to be noted. By substituting the above

values in the formula the radius of curvature of the given lens can be found.

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Graph:

Precautions :

(1) Glass plates and Lens should be cleaned.

(2) The lens used should be of large radius of curvature.

(3) The source of light should be an extended one.

(4) The rings formed should be well defined and clear.

(5) Before measuring the diameters of the rings, the range of the microscope should be

properly adjusted.

(6) Cross wire should be focused on a dark ring tangentially.

Result :

The radius of curvature of the plano-convex lens has been determined by forming Newtons

rings. Its valu from the graph is _________cm.

Lecturer signature with Date:

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Roll No:

Observations :

Least count of the traveling microscope = 1 Main scale division value

No. of vernier scale divisions

No. of

the Dark

ring

MICROSCOPE READINGS when the vertical cross wires coincides with

the

Diameter of the

ring

D =d1~d2 cm.

D²

Left end of the ring Right end of the ring

M.S.R.

a cm.

V.C.

n

Total reading

d1=a+(nχl.c) cm.

M.S.R.

a cm.

V.C.

n

Total reading

d2=a+(nχl.c) cm.

21

18

15

12

9

6

3

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Roll No:

Date:

2. RESOLVING POWER OF A TELESCOPE

Aim : To determine the resolving power of a telescope.

Apparatus : Telescope, sodium light, wire-gauze with fine uniform mesh, a rectangular slit

whose width can be adjusted, travelling microscope and meter scale.

Principle : The resolving power of a telescope is its ability to form separate and distinguishable

images of two point objects situated very close to each other.

The resolving power is measured by the smallest angle subtended at the objective of the

telescope by two point objects which can be seen just separate and distinguishable. Smaller is

this angle, higher is the resolving power of the telescope.

Formula : The theoretical and practical resolving powers are given by

Theoretical resolving power = λ/a and

Practical resolving power = d/D

Where λ = mean wave length of light USed,

a = width of the rectangular slit for when the two objects are just resolved..

d = separation between two objects.

D = distance of the objects from the objective of the telescope.

Hence,

λ = d

a D

Figure:

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Theory :

Rayleigh’s criterion of resolution : According to Rayleigh’s criterion, two equally bright

sources which are very closely situated can be just resolved by any optical system when their

distance apart is such that in the diffraction pattern, the central maximum due to one falls on the

first diffraction minimum due to the other.

Procedure :

1. Mount the telescope on a stand such that its axis lies horizontal and the wire gauge on

another stand such that they are vertical. Place the two stands at a suitable distance.

2. Illuminate the object with source of light. Fix the slit in front of the objective of the

telescope. Now open the slit with the help of micrometer screw and move the telescope in the

horizontal direction such that the images of the two vertical wires are in the field of view of

the eye piece. The horizontal wires will also be seen.

3. Gradually reduce the width of the slit moving the micrometer screw only in one direction till

the horizontal wires are only seen. i.e., when the vertical wires disappear Then note the

reading of the micrometer(Q). Again move the micrometer screw of the slit in the same

direction till the slit is completely closed. Note the reading of the micrometer(R). The

difference between the two readings of the micrometer gives the width of the slit ‘a’ just

sufficient to resolve the two images. Note the distance between the slit and the wire gauge

‘D’. The observations are tabulated in the table-1. Repeat the experiment for different values

of ‘D’.

If the micrometer screw has an error, the width of the slit can be measured by using a

travelling microscope. After the vertical cross wires just disappear, remove the slit from the

objective and focus it in front of the traveling microscope. When the slit comes into the field of

view of the microscope, make the vertical crosswire in the eye piece of the traveling microscope

coincide with one edge of the slit say (left hand edge). Note the reading in the traveling

microscope. Move the traveling microscope so that the vertical cross wire coincides with the

right hand side (R.H.S) edge. The difference between these two readings gives the width of the

slit ‘a’. Note the observations in table-2. Measure the distance between the slit and the wire

gauge ‘D’. Repeat the experiment for different values of ‘D’.

4. Measure the width ‘d’ of vertical wires with the help of a travelling microscope. Note the

observations in table-A.

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Precautions and sources of error :

1. The axis of the telescope should be horizontal.

2. The rectangular slit should be parallel to the vertical lines of the wire gauge.

3. The wire gauge should be vertical.

4. Backlash error in the micrometer screw should be avoided.

5. The width ‘a’ should be measured carefully.

6. The minimum width of the slit for resolution should be adjusted very carefully.

7. The distance D should be measured from the slit of the telescope to the wire gauge.

Result :


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POSSIBLE VIVA QUESTIONS

1. What do you mean by resolving power of a telescope ?

2. On what factors does the resolving power of a telescope depend.

3. Why are telescopes fitted with objectives of large diameter?

4. What is the resolving power of the eye?

5. Does the resolving power of a telescope depend upon the focal length of its objective?

6. Does the resolving power of a telescope depend upon the distance between the telescope

and the object to be resolved?

7. What is telescope?

8. What are its parts

9. What is Rayleigh’s criteria.

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Roll No:

Observations :

1. Wave length of light λ = 5893 X 10-8 cm.

Table for distance between two adjacent wires ‘d’:

Least count of traveling microscope = cm.

Table-A:

Number of

the

vertical

wire on

the mesh

Microscope reading

‘a’ (when the

vertical cross wire

in the eye piece

coincides with the

vertical wire on the

mesh)

M.S.R.+(V.CXL.C)

cm

Number of

the vertical

wire

Microscope reading ‘b’

(when the vertical

cross wire in the

eye piece coincides

with the vertical

wire on the mesh)

M.S.R.+(V.CXL.C)

cm

Distance

between ‘5’

Vertical

wires.

a ~ b

Distance

between two

adjacent wires

d = a ~ b cm.

5

1

6

2

7

3

8

4

9

5

10

Average d = cm.

Table for measuring the width of the slit ‘a’:

Least count of the micrometer = mm. = cm.

Table-1:

S.No.

Distance between

the slit and wire

gauge

D cm.

Micrometer Readings Width of the

slit

a = Q - R cm.

d/D λ/a

when the vertical

wires disappear

(Q)

PSR+(HSRXLC)

cm

When the slit is

closed (R)

PSR+(HSRXLC)

cm

1

2

3

110

120

130

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4

5

140

150

Table for measuring the width of the slit ‘a’ using traveling microscope:

Table-2:

S.No.

Distance

between the

slit and wire

gauge

D (cm)

Travelling microscope reading

When the vertical cross wire coincides

the

Width of

the slit

a = R1~R2

cm.

d/D λ/a

L.H.S of the slit

(R1) cm

M.S.R+(V.CXL.C)

R.H.S of the slit

(R2) cm

M.S.R+(V.CXL.C)

1

2

3

4

5

110

120

130

140

150

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Roll No:

Date:

3. DISPERSION OF LIGHT – CAUCHY’S CONSTANTS

Aim : To study the dispersion of light through the prism and evaluate the Cauchy’s constants.

Apparatus : Reading lens, prism, spirit level, mercury lamp and spectrometer.

Formula : Cauchy showed that the variation of refractive index μ of the material of the prism

of the light incident with wavelength λ can be represented by the relation

μ = A + B ---------(1) λ2

The constants A and B can be obtained from the graph and also by the formulae

A = μ1 - B = μ2 - B ---------(2) λ1 λ2

B = (μ1- μ2) ---------(3)

1 - 1

λ1 λ2

Where μ1 and μ2 are the refractive indices of the material of the prism for wave lengths λ1

and λ2 respectively.

The value of μ for a particular wave length can be calculated by using the formula

Sin (A+δm) μ = 2 ----------(4)

Sin A/2

Where A = Angle of prism and δm = Angle of minimum deviation.

Dispersive power:

Dispersive power of a medium is defined as the ratio between the angular dispersion for the two

colours and the mean deviation

δv – δr δv + δr

W = δ where δ = 2

δv, δr are angular dispersion for violet and red colour.

For a prism of small refracting angle (A) the deviation δ = (μ -1)

w = μv – μr (μ -1)

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DESCRIPTION OF THE APPARATUS :

Spectrometer: The spectrometer consists of the following parts:

(i) The collimator C,

(ii) The prism table P,

(iii) The telescope T.

(i) The collimator : The collimator C consists of two hollow concentric metal tubes, one being

longer than the other. The longer tube carries an achromatic lens L at one end and the smaller

tube on the other end. The smaller tube is provided with a variable slit at the outer end and can

be moved in or out the longer tube with the help of rack and pinion arrangement. The slit is

adjusted in the focal plane of the lens L to obtain a pencil of parallel rays from the collimator

when light is incident on the slit. The collimator is also provided with two screws for adjusting

the inclination of the axis of the collimator. This is rigidly fixed to the main part of the apparatus.

(ii) The prism table : It is a circular table supported horizontally in the centre of the instrument

and the position can be read with the help of two verniers attached to it and move over a

graduated circular scale carried by the telescope. The levelling of the prism table is made with

the help of three screws provided at the lower surface of the table. The table can be raised or

lowered and clamped in any desired position with the help of a screw. The prism table is also

provided with a tangent screw for slow motion. There are concentric circles and straight lines

parallel to the line joining two of the levelling screws on the prism table.

(iii) The telescope : The telescope consists of similar tubes as in case of collimator carrying

achromatic objective lens O at one end and Ramsden eye piece E on the other side end.

The eye piece tube can be taken in or out with the help of rack and pinion arrangement. Two

cross wires are focused at the focus of the eye piece. The telescope can be clamped to the main

body of the instrument and can be moved through a small angle using the tangent screw. The

telescope is attached to the main circular scale and when it rotates, the graduated scale rotates

with it. The inclination of telescope is adjusted by two screws provided at the lower surface.

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Adjustment : Before using the spectrometer, the following adjustments must be made.

(a) The axis of the telescope and that of the collimator must intersect the principal vertical axis

of rotation of the telescope. (this adjustment is done by the manufacturer)

(b) Prism table should be levelled.

The prism table is levelled with the help of three screws supporting the prism table. A spirit

level is placed along a line joining the screws and the two screws are moved till the air bubble

appears in the middle. Now place the spirit level along a line perpendicular to the previous line

and adjust the third screw such that again the air bubble appears in the middle. Now first two

screws should not be touched this time. The prism table is now levelled.

Procedure :

(i) Determine the least count of the spectrometer.

(ii) Place the prism so that its centre coincides with the centre of the prism table and light

falls on one of the polished faces and emerges out of the other polished face, after

refraction. In this position the dispersion of light taken place and we get a spectrum of the

incident light.

(iii) The spectrum is seen through the telescope. The telescope is adjusted for minimum

deviation position for a particular colour (wave length) in the following way :

(iv) The measurements are taken after the telescope is adjusted for minimum deviation

position for d particular colours.

Set up the telescope so that the vertical cross wire of the eye piece coincides with the

mean colour i.e. yellow now rotate the prism lab, in any one direction slowly making sure

that the telescope is moved so that the spectrum is always in the view. By doing this we

find that the spectral line initially moves in one direction and at a particular position starts

retreating in the opposite direction although the rotation of the prism table is adjusted in

the same direction.

Note the reading of the two verniers.

(v) Remove the prism and bring the telescope in the line of the collimator. See the slit

directly through telescope and coincide the image of slit with vertical cross wire. Note the

readings of two verniers.

(vi) The same procedure is repeated to obtain the angles of minimum deviation for other

colours.

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Roll No:

Graph : Evaluation of constants A & B from graph

A = OP , B = SR/QR

Dispersive power

W = μv – μr (μ -1)

Where μv and μr are the refractive indices of the material for violet and red colours.

Precautions :

(i) The telescope and collimator should be individually set for parallel rays.

(ii) Slit should be as narrow as possible, but should be of sufficient brightness.

(iii) While taking observations, the telescope and prism table should be clamped with the help

of clamping screws.

(iv) Both verniers should be read.

(v) The prism should be properly placed on the prism table.

(vi) There should be no parallax error between the vertical cross wire and the image of the

slit.

Result:


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Observations :

(i) Value of the one division of the main scale = 0.5 degree.

(ii) Total number of vernier divisions = 30

Least count of the vernier = 0.5/30 = 1 minute.

Angle of the prism A = 60.

Ver 1 Ver 2

Direct reading of the spectrometer R1 = R2 =

S.No.

Colour

Wavelength

λ cm.

Deviated Reading Angle of minimum

deviation

δm =R1~D1+R2~D2

2

Sin (A+δm)

μ = 2

Sin A/2

1

λ2 MSR V.C Total=MSR+

(V.C x LC)

1

2

3

4

5

6

7

8

9

Violet1

Violet2

Blue

Bluish

Green

Green

Yellow 1

Yellow 2

Orange

Red

4046x10-8D1

D2

4078x10-8D1

D2

435x10-8 D1

D2

4916x10-8D1

D2

5461x10-8 D1

D2

5770x10-8D1

D2

5791x10-8D1

D2

6152x10-8D1

D2

6908x10-8D1

D2

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Possible viva questions

1. Why should we take readings from the two verniers on the circular scale.

2. when the prism is in the minimum deviation position, how will be the path of the light ray

inside the prism.

3. what is the need for adjusting the collimator to renden light rays parallel and telescope to

catchs the parallel light rays.

4. what is a pure spectrum

5. what is a source of monochromatic light? Is the sodium vapour lamp such a source of

monochromatic light

6. what is dispersion of light

7. Define angle of deviation

8. Define refractive index.

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Roll No:

Date:

4. REFRACTIVE INDEX OF A LIQUID

Aim : To determine the refractive index of a liquid using a hollow prism and laser source.

Apparatus : laser source, hollow prism, rotating stand, liquid.

Sin A+Dm)/2

Formula : = -----------------

Sin (A/2)

Where A = Angle of prism = 60

Dm = Angle of minimum deviation.

LASER: Light Amplification by Stimulated Emission of Radiation.

LASER is a source of monochromatic radiation.

Lasers are highly

1. Monochromatic

2. Directional

3. Spacially and temporally coherent

4. Intense

The power of the solid state laser and semiconductor lasers we are using is 2 to 3 mw.

N1N2 , M1M2 normals to the refracting surfaces at the point of incidence and point of emergence.

i1 angle of incidence.

i2 angle of emergence.

Theory : The deviation produced by a prism is minimum when

1) The angle of incidence is equal to the angle of emergence

i1 = i2 = i

2) The angle of refraction at the first surface is equal to the angle of incidence at the

second surface.

r1 = r2 = r

3) The path of the ray inside the prism is parallel to the base of the prism.

At minimum deviation position:

The angle of the prism A = r1 + r2 = 2r or r = A/2

For an equilateral prism A = 60

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Roll No:

The angle of deviation D = (i1 + i2) A

The angle of minimum deviation Dm = 2i A , i = (A+Dm)/2

Sin (A+Dm)/2

Hence = sin i/sin r = ----------------

Sin (A/2)

Procedure :

1. Keep the prism on a rotating stand with one of its refracting surfaces facing the laser light.

See that the axis of rotation of the stand passes through the centre of the prism.

2. Let the laser light fall on the refracting surface of the prism normally.

3. Adjust the prism by rotating the table so that the deviated image from the other refracting

surface is seen on the wall.

4. Now looking at the image rotate the prism table so that the deviated image moves closest to

the direct spot (this is the spot of the Laser beam on the wall without the prism). This

position of the deviated image, is the minimum deviation position.

5. Now measure the perpendicular distance between the centre of the prism and the wall (x),

also measure the distance between the direct spot and the image at minimum deviation

position(y).

6. Repeat the same procedure by keeping the second refracting surface, facing the laser beam.

7. Repeat the whole experiment for different values of ‘x’.

Precautions :

1. Handle the Laser source carefully as it is very expensive.

2. Do not look at the laser beam directly.

3. Locate the minimum deviation position accurately.

Result :


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Roll No:

Angle of prism A =60°

S.No.

Distance

between the

centre of the

Prism and the

wall

X ( cm)

Distance between the direct

spot and deviated image at

min. deviation position ‘y’

(cm)

y/x

Dm = Tan-1 (y/x)

Sin(A+Dm)/2

= ----------- Sin(A/2)

Left Right Mean

1

2

3

4

5

Average =

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Roll No:

Date:

5.STUDY OF MONOCHROMATIC DEFECTS OF IMAGES

Aim :

To determine the longitudinal spherical aberration and longitudinal chromatic

aberration of a convex lens.

Apparatus :

A convex lens, sodium vapour lamp, optical bench, a screen, wire-gauze, mercury lamp and

stops(card boards of different diameters), filters.

Formula :

1.Longitudinal spherical aberration = fp - fm ---------(1)

2.Longitudinal chromatic aberration= fR - fB ---------(2)

Where fp = paraxial focal length of the convex lens

fm = marginal focal length of the convex lens

fR = focal length of the convex lens for Red colour

fB = focal length of the convex lens for Blue colour

Theory :

Parallel rays after passing through the convex lens converge at different points on the

principal axis. The rays which are close to the principal axis are called paraxial rays and the rays

which are away from the principal axis are called marginal rays. The lens can be divided into

circular zones. So, different zones have different focal lengths. The marginal rays after

refraction come to a focus on the principal axis at Fm . The distance between Fm and the optic

centre is called the marginal focal length fm. The paraxial rays meet the principal axis at Fp and

the distance between Fp and the optic centre is called the paraxial focal length fp. Thus, the

paraxial rays form the image at a point which is farther than the focal point due to marginal rays.

Therefore, the image is not sharp at any point on the axis. This defect is called spherical

aberration. The difference between fp and fm gives the longitudinal spherical aberration.

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Description :

The experimental arrangement is shown in figure. The optical bench consists of a long

heavy metal base MN (cast iron) of double rod type (rails) nearly 2 meters long. One arm of the

bench is graduated in millimeters. Four levelling screws are provided at the base of the bench by

means of which the optical bench can be made horizontal. Four metal uprights (or stands) are

mounted on the bench, which can be moved along the rails on the bed of the bench and can be

fixed at any desired position with clamping screws. All the uprights are provided with a rack and

pinion arrangement with the help of which, they can be raised or lowered and fixed at any

desired height. The position of upright on the graduated scale can be noted with the vernier

provided at the base of each upright. The uprights are used to mount the various components

(accessories) like the slit, the wire gauze (object), convex lens and the screen.

Fig.(2)

Procedure :

1.To determine the longitudinal spherical aberration

Level the optical bench so that it is perfectly horizontal by means of the leveling screws and

spirit level. Take a convex lens of focal length about 20cm, mount it on one of the uprights and

place it at distance of 40 cm from the object. Mount the object (wire- gauze ) on the second

upright and place it between the convex lens and slit. The screen is to be placed on the fourth

upright beyond the convex lens in order to observe the image of the object. Place the slit of

variable width on one of the uprights at one end of the optical bench. Illuminate the slit with

sodium vapour lamp. Reduce the width of the slit and rotate it in its own plane, about an axis

parallel to the axis of the bench with the help of a tangent screw until the slit becomes vertical.

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Take a thin round card board and make a small circular hole at its centre. Fix this card

board on one side of the lens with gum. Due to this, only paraxial rays are allowed to pass

through the lens whereas the marginal rays are cut off. Adjust the distance of the screen until a

clear and bright image of the object is formed on the screen. Then, note the distance u of the

object from the lens and the distance v of the image from the lens. The paraxial focal length fp of

the lens can be calculated using the formula,

f p = u v / (u + v ) --------------(3)

Repeat the experiment 3 or 4 times by placing the object at various distance say 43cm,

46cm and 49cm and in each case measure the corresponding image distance v as well as the

paraxial focal length fp . Find the average paraxial focal length. Note the observations in table 1.

Now, take a thin circular card board of small diameter and fix it to one side of the lens with

gum or paste. Due to this, only marginal rays are refracted through the lens and paraxial rays are

cut off. Place the wire-gauze at a distance u (say 40cm) from the convex lens. Repeat the same

procedure as was adopted above and note the image distances by placing the object at 43 cm,

46cmand 49cm. find the average marginal focal length fm . Note the observations in table 2. the

longitudinal spherical aberration can be calculated using the formula fp-fm.

2.To determine the longitudinal chromatic aberration

In order to find out the longitudinal chromatic aberration, replace the sodium light by

mercury vapour lamp and mount the micrometer eye-piece on one of the uprights. Now,

interpose a red filter in between the source and the slit. The red filter allows light of single

wavelength which falls in the red region. Place the convex lens at a distance u (say 30cm) from

the slit. Adjust position of the eye-piece until the red image of the slit is clearly visible. Note the

distance of the image v from the lens. The focal length fR of the lens for red colour can be

calculated using the formula fr = uv / (u+v). Repeat the experiment by keeping the lens at various

distances say 33cm,36cm and 39cm. Find the average focal length of the lens for red colour.

Tabulate the observations in table 3. Now, remove the red filter, introduce the blue filter and

repeat the experiment as was done above and find the average focal length fB of the lens for blue

colour. Tabulate the observations in the table 4. The longitudinal chromatic aberration can be

calculated using formula fr-fB.

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Precautions :

1.The optical bench should be made perfectly horizontal using the leveling screws and the spirit

level.

2.The slit should be vertical and narrow. The slit should be erected parallel to the wire-gauze.

3.All the uprights should be mounted at the same height.

The filters should not be over exposed to the radiation.

Result:

Lecturer signature with date:

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Roll No:

Observations :

Table 1: To determine the paraxial focal length fp of the convex lens

S.No Object distance u cm Image distance v cm f p =uv/(u+v) cm

1 40

2 43

3 46

4 49

Average paraxial focal length of the convex lens, fp = cm

Table 2 : To determine the marginal focal length fm of the convex lens

S.No Object distance u cm Image distance v cm f m = uv/(u+v) cm

1 40

2 43

3 46

4 49

Average marginal focal length of the convex lens, f m = cm

Longitudinal spherical aberration is fp-fm= cm

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Table 3 : To determine the focal length f R of the convex lens for red colour

S.No Object distance u cm Image distance v cm f R =uv/(u+v) cm

1 30

2 33

3 36

4 39

Average focal length of the convex lens for red colour fR = cm

Table 4 : To determine the focal length fB of the convex lens for blue colour

S.No Object distance u cm Image distance v cm fB = uv/(u+v) cm

1. 30

2. 33

3. 36

4. 39

Average focal length of the convex lens for blue colour fB = cm

Longitudinal spherical aberration is fr-fb= cm

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Date:

7. CARDINAL POINTS

Aim : To locate the cardinal points of a coaxial optical system of two thin convergent lenses

separated by a distance and to determine the focal length using Newton’s formula.

Apparatus : Optical bench, plane mirror, cross slit, lamp, Nodal slide

Formulae : If f1 and f2 are the focal lengths of the two lenses L1 and L2, x the distance between

them and F the focal length of the lens combination, then we have,

XF

Distance between the first lens and the first nodal point. L1N1 = + ---- ----------------(1).

f2

XF

Distance between the second lens and the second nodal point. L2N2 = − ------ --------------(2)

f1

Where N1 and N2 are the positions of the first and second principal points or nodal points

of the lens system and L1, L2 are the positions of the lenses.

Figure :

Description : This is an optical bench with the nodal slide . It consists of an optical bench with

an upright for a lamp, and another upright has got a cross-slit on a metallic plate. The slit is

illuminated by the lamp and the illuminated cross–slit acts as the object. The upright carrying

two lenses is the nodal slide. The positions of the lenses can be varied and read on a scale. The

scale can be rotated about an axis of rotation the position of which can be read on the optical

bench. The fourth upright holds a plane mirror.

The cardinal points of a coaxial optical system consists of a set of two focal points,

two principal points and two nodal points.

Procedure: The focal lengths of the two lenses are found out by the optical bench. One lens is

mounted on the nodal slide and its position is adjusted so that the image of the cross-slit is

formed on itself after reflection from the plane mirror. The distance between the cross-slit and

the lens will be the focal length of the lens. The same is repeated with the other lens.

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Roll No:

The focal lengths of the individual lenses are found out by plane mirror method. They are then

mounted together at a distance ‘d’ from each other with a plane mirror on one side as L1F1. The

image of the object is thus formed in its own plane and the distance between the first lens and the

image is noted. This is the first focal point. Then the nodal slide is given a 180o rotation so that

the second lens faces the object. The system is adjusted. So that the image is again formed on the

object plane, and the distance between the image and the second lens is noted as L2F2 . The nodal

system is turned back to its original position so that L1 faces the object.

Move the nodal system through a distance from the object place a screen behind the nodal slide

and obtain the image of the object. Measure the distance between the first lens and object as L1O,

and the distance between the second lens and image as L2I. L1O−L1F1 gives x1 and L2I−L2F2

gives x2. Then the focal length of the combination of lenses is obtained by the formula F =

√(x1x2). This is called Newton’s formula.

F = √(x1x2). (Newton’s formula)

The focal length of the combination, F is also found by mounting the two lenses

together on the nodal slide separated by a known distance. The combination is then adjusted to

get an image on the cross-slit itself by placing the plane mirror behind the nodal slide. The whole

assembly is given a small rotation. The image will be found to shift on the screen. The assembly

is then moved and adjusted such that any small rotation does not produce any shift of the image.

After that the upright of the assembly is moved to produce a well focused sharp image of the

cross-slit. In this position, the distance between the cross- slit (position of second focal point, F2)

and the axis of the nodal slide (position of the second nodal point, N2) on the optical bench will

give the focal length of the combination. This distance is N2I, if L2 is towards the cross-slit as in

the figure or N1O if the lens L1 is towards the cross-slit.

When no lateral shift position is obtained and the image is well focused, the cross –

slit will lie in the second focal plane and the axis of rotation i.e., the upright of the assembly will

pass through the second nodal point of the combination.

Since the medium on both sides of the lenses is air, the principal points coincide

with the nodal points and so the position of both is the same. It is denoted by N2. The above

procedure is repeated for different values of d. (distance between the two lenses).

(1) Plotting the cardinal points

(2) Nodal slide : Equivalent focal length F = N1I

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Roll No:

Precautions:

1. Some times a bright image is formed on the screen by reflection from lens surface. This

should not be confused with the genuine image which is formed by the light passing

through the lenses and reflected from the mirror. On slightly turning the mirror the

genuine image will shift whereas the false image remains fixed or when the mirror is

closed with your hand the image disappears.

2. The rotation of the nodal slide about the vertical axis should be very small not exceeding

5.

3. The lenses should be mounted such that the principal axis passes through the intersection

of the cross-slit and is parallel to the optical bench. 4. The mirror should be truly plane. 5. Image should be very sharp. 6. Lenses with large focal length should be used for better results.

Result:


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Roll No:

Observations :

(1) Focal length of the first lens f1 =

(2) Focal length of the second lens f2 =

Table for equivalent focal length F, L1N1 and L2N2:

S.No

.

d cm L1F1

cm

L2F2

cm

L1O

cm

L2I

cm

x1 =L1O-L1F1

cm

x2=L2I-L2F2

cm F=√x1x2

cm

L1N1 =

F-L1F1

Cm

L2N2=

F-L2F2

cm

1

4

1)

2)

3)

2

6

1)

2)

3)

3

8

1)

2)

3)

d – distance between the two lenses

L1F1 – distance between the first lens and the first focal point

L2F2 – distance between the second lens and the second focal point

L1O – distance between the first lens and the object

L2I – distance between the second lens and the image.

F- Combined focal length

L1N1 – distance between the first lens and the first Nodal point

L2N2 – distance between the second lens and the second Nodal point

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Roll No:

Verification :

Theoretical Observed Observed Theoretical Observed Theoretical Observed

S.No d

cm

f1f2

F= ---------

f1+f2-d

cm

F=√x1x2

Cm

F=N1O

or

N2I

cm

L1N1=F.d/f2

cm

L1N1 =

F-L1F1

Cm

F.d

L2N2= ----

f1

cm

L2N2=

F-L2F2

cm

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Roll No:

Date:

8. REFRACTION – SNELL’S LAW

Aim: To verify the Snell’s law by varying angles of incidence and angle of reflection in different

media using computer simulation, and also determine the critical angle of different media.

Procedure: a) Click start

b) Double click phy practicals

c) Double click ph(11e)

d) Double click ph(11e)

e) Double click Refraction experiment.

1. Read the instructions given on the screen completely to start the experiment.

2. Select two different media with their values of refractive indices 1, 2

3. Case 1) Keep the first medium constant and vary the second medium note down the

values of angle of incidence, angle of reflection , angle of refraction.

4. Repeat the experiment for three different sets of media and tabulate the readings.

5. Case 2) Repeat, step 3,4 by keeping the second medium constant and varying the first

medium.

6. Tabulate all values in the table provided, calculate and verify Snell’s law.

7. Take first medium as a denser medium and the second medium as a rarer medium.

Eg: glass with = 1.5 and water with = 1.35. Do the experiment and note the critical

angle for glass. Repeat for different sets of media.

Result:

Lecturer signature with date:

32



Roll No:

Observation:

Total Internal reflection:

S.No Medium Refractive index Critical angle

1 Denser – glass

Rarer – water

2 Denser ethanol

Rarer – air

3 Denser – glass

Rarer - air

S.No

Medium

with the

values of

refractive

index

Refractive

Index

Angle of

incidence

( i )

Angle of

reflection

Angle of

refraction

( r)

Sin i Sin r

Observed

12 = Sin i

Sinr

Theoretical

12 = 2

1

1.

Air - I

Water - II

2.

Air- I

Quartz

glass- II

3.

Air- I

Ethanol- II

4.

Water- I

Ethanol- II

5.

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Roll No:

Date:

ABSORPTION SPECTRUM OF IODINE VAPOUR

Aim: To study the absorption spectrum of iodine vapour.

Apparatus: Incandescent lamp, glass tube of (one meter) length with iodine grains inside,

spectrometer, diffraction grating.

Formula: The wavelength of an absorption band can be estimated from the grating formula

d Sinθ = nλ Where d is the spacing between two opaque lines on the grating ---(1)

λ = 2.54 Sin θ / Nn cm. d = 2.54/N

Here θ = The angular position of the absorption band of wavelength λ, or angle of diffraction

N = Number of lines per inch length of grating and

n = order of the spectrum.

The energy levels of the iodine molecules can be calculated from.

That E = h = h c / λ

With λ in meters and c= velocity of light in vaccum

= 3 X 108 m/s and

Planck’s constant h = 6.62 X 10-34 J.S

We get E in joules.

The arrangement for the experiment will be as shown in figure (1).

Description of apparatus and Theory of Experiment :

The glass tube T contains some fine iodine grains in it. Even at room temperature the iodine

grains get vapourised and the iodine atoms will be in their ground state. When white light

(containing all wavelengths) is incident on the iodine vapour, the iodine molecules absorb those

wavelengths from the incident light which correspond to the energy difference between the

ground state and different excited states of iodine molecules. This is, corresponding to

E excited – E ground = h = hc /

Thus we get an absorption spectrum of iodine. In the back ground of the continuous spectrum

of white light, we get a series of dark lines – or more precisely bands as we are dealing with

iodine molecules.

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Roll No:

With the help of a diffraction grating and spectrometer, we can measure the angle of

diffraction ‘’ and evaluate the wave length λ from = Sin / Nn. from this E = hc / is

calculated.

PROCEDURE : An incandescent lamp L is mounted inside a housing H having an opening at

O. this should be along the axis of the collimator. The spectrometer adjustments are carried out

and the grating is also adjusted for normal incidence as explained below. Initially, with the light

coming out from the incandescent lamp, we observe through the telescope a continuous

spectrum.

Next we introduce the glass tube T containing some fine iodine grains inside it in between

the lamp and the collimator of the spectrometer. Due to absorption of certain wavelengths of

white light by the iodine molecules, dark bands are now observed through the telescope in a back

ground of the continuous spectrum.

Measurements are to be made from the farthest available band on the longer wavelength side

because the successive bands are very close to each other. Count the farthest band as n in number

and take its reading on the circular scale as T1. Now, come to the central part at equal intervals

of 5 bands each, counting them from the farthest n as n+5,n+10, n+15…….n+30 and take T1

readings at each band.

PRECAUTIONS:

1. All precautions which have been taken for spectrometer in Cauchy’s constant experiment.

2. Don’t touch the Glass tube when it is in use

3. Don’t touch the bulb

4. As there is a usage of H.T Input supply do not touch the bare electrical wires.

RESULT:

Lecturer Signature with Date:

35



Roll No:

OBSERVATIONS:

Note: After normal incidence adjustement is done direct reading of the telescope

V1 = V2=

1.M.S.D. on circular scale = 1/2 = 30

No. of vernier scale divisions = 30

L.C of the vernier = 30/30 = 1

Table 1: Readings of the positions of the telescope

When the vertical cross wire coincides with the dark band

Serial No. of the dark

band

Telescope on the left side T1 Telescope on the right side T2

V1 V2 V1 V2

n

n+5

n+10

n+15

n+20

n+25

n+30

Angle of diffraction

1 = (T2 – T1)

2

of V1

2 =

(T2 – T1 ) / 2 of

V2

Mean =

(1+2) / 2

Wavelength of the line

= 2.54 Sin cm

Nn

Energy observed

E = hc / (J)

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Roll No:

1. newton’s rings -...

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