Sastry CBSE

To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and the angle of deviation

Physics Lab ManualNCERT Solutions Class 12 Physics Sample Papers

Aim
To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and the angle of deviation.

Apparatus
Drawing board, a white sheet of paper, prism, drawing pins, pencil, half-metre scale, office pins, graph paper and a protractor.

Theory
The refractive index in) of the material of the prism is given by

where, D_m angle of minimum deviation and A angle of the prism.

Diagram

Procedure

1. Fix a white sheet of paper on the drawing board with the help of drawing pins or tape.
2. Draw a straight line XX’ parallel to the length of the paper nearly in the middle of the paper.
3. Mark points Q₁, Q₂, Q₃,… on the straight line XX’ at suitable distances of about 5 cm.
4. Draw normals N₁Q₁, N₂Q₂, N₃Q₃,… on points Q₁, Q₂, Q₃,…  as shown in diagram.
5. Draw straight lines R₁Q₁, R₂Q₂, R₃Q₃,… making angles of 35°, 40°, … 60° (write value of the angles on the paper) respectively with the normals.
6. Mark one comer of the prism as A and take it as the edge of the prism for all the observations.
7. Put it prism with its refracting face AB in the line XX’ and point Q₁ in the middle of AB.
8. Mark the boundary of the prism.
9. Fix two or more office pin P₁ and P₂ vertically on the line R₁Q₁. The distance between the pins should be 10 mm or more.
10. Look the images of point P₁ and P₂ through face AC.
11. Close your left eye and bring open right eye in line with the two images.
12. Fix two office pins P₃ and P₄ vertically, and 10 cm apart such that the open right eye sees pins P₄ and P₃ and images of P₂ and P₁ in one straight line.
13. Remove pins P₃ and P₄ and encircle their pricks on the paper.
14. Repeat steps 7 to 13 with points Q₂, Q₃,… for i = 40°,…, 60°.
    To measure D in different cases
15. Draw straight lines through points P₄ and P₃ (pin pricks) to obtain emergent rays S₁T₁,S₂T₂,S₃T₃,……
16. Produce T₁S₁, T₂S₂, T₃S₃, … inward in the boundary of the prism to meet produced incident rays R₁Q₁, R₂Q₂, R₃Q₃,… at points F₁, F₂, F₃,…
17. Measure angles K₁F₁S₁,K₂F₂S₂,K₃F₃S₃,…….. These give angle of deviation D₁,D₂,D₃,….
18. Write values of these angles on the paper.
    To measure A
19. Measure angle BAC in the boundary of the prism. This gives angle A.
20. Record your observations.

Observations
Angle of prism ‘A’ =……

Calculations
Plot a graph between angle of incidence ∠i and angle of deviation ∠D by taking ∠i along X-axis and ∠D along Y-axis. From this graph, find the value of single of minimum deviation D_m corresponding to the lowest point of the graph.

Result

1. i-D graph indicates that as the angle of incidence (i) increases, the angle of deviation (D) first decreases, attains a minimum value (D_m ) and then starts increasing for further increase in angle of incidence.
2. Angle of minimum deviation, D_m = ……..
3. Refractive index of the material of the prism, n = ……….

Precautions

1. The angle of incidence should lie between 35°-60°.
2. The pins should be fixed vertical.
3. The distance between the two pins should not be less than 10 mm
4. Arrow heads should be marked to represent the incident and emergent rays.
5. The same angle of prism should be used for all the observations.

Sources of error

1. Pin pricks may be thick.
2. Measurement of angles may be wrong.

VIVA VOCE

Question. 1.Define a prism.
Answer.Read Art. 9.04.

Question. 2.Define edge of the prism.
Answer.Read Art. 9.04.

3.Question. .Define angle of prism.
Answer.Read Art. 9.04.

Question. 4.Define angle of deviation.
Answer.The angle through which a ray of light turns away from its original path on passing through a prism, is called angle of deviation.

Question. 5.On what factors does the angle of deviation depend?
Answer.The angle of deviation depends upon the following factors :

1. The angle of incidence.
2. The refracting angle of the prism.
3. The material of the prism. (Refractive Index)
4. The colour of the light used i.e., wavelength of light.

Question. 6.What is the relation between different angles involved in refraction through a prism?
Answer. Read Art. 9.05.

Question. 7.Define angle of minimum deviation.
Answer.The least value of the angle of deviation is known as the angle of minimum deviation. [Art. 9.06 (a)]

Question. 8.How is angle of minimum deviation related with refractive index of prism material?
Answer. Read Art. 9.06 (b).

Question. 9.What is the speciality about minimum deviation?
Answer.Under minimum deviation condition, light ray travels inside prism parallel to the base of the prism and the angle of incidence = angle of emergence.

Question. 10.Does the angle of minimum deviation depend upon the colour of light used?
Answer.Yes, it is different for different colours or wavelengths.

Question. 11.What word helps in remembering the name of seven colours into which white light is splitted?
Answer.The word is VIBGYOR.

Question. 12.What name is given to the phenomenon of splitting white light into seven colours?
Answer.The phenomenon is called dispersion of light.

Question. 13.What does the graph between i and D indicate?
Answer.There is only one unique value of angle of incidence for which the deviation is minimum.

Question. 14.Why there are two values of angle of incidence for one value of angle of deviation?
Answer.If the emergent ray be reversed, then angle e becomes i and angle i becomes e. The reversed ray will have same deviation as before.

Question. 15.Hence, i and e are two different values for same angle of deviation.
Which colour will travel (i) fastest (ii) slowest in prism?
Answer.(i) Red colour (ii) Violet.

Question. 16.Does a beam of white light give a spectrum on passing a hollow prism?
Answer.No. Because dispersion does not occurs in air.

Question. 17.Which colour deviate (i) Most (ii) Least.
Answer. (i) Violet (ii) Red.

Question. 18.Will all colour of light travel with same speed inside a prism?
Answer.No. Red colour travel fastest and violet colour travel smallest.

Question. 19.Which colours have hightest and smallest refractive index? Why?
Answer.Refractive index is smallest for red colour and that is highest for violet colour

Question. 20.What is Cauchy relation?
Answer.It is the relation between refractive index of a transparent medium and colour of light.

Question. 21.Can X-rays be dispersed?
Answer.Yes.

Question. 22.What is angular deviation?
Answer.The angle between the emergent rays of any two colours is called angular dispersion of those colours.

Question. 23.On what factors angular deviation depends?
Answer.(i) Angle of prism (ii) refractive index.

Question. 24.What is dispersive power of prism?
Answer.It is define as the ratio of the angular dispersion for these two colours to the mean deviation produced by the prism.

Question. 25.What is factor on which dispersive power depends?
Answer.It depends upon refractive index of the material of prism.

Slab
A slab is a piece of transparent material with rectangular faces. All faces are transparent and opposite faces are parallel.
The dimension (side) along which the light travels inside the slab is called its thickness.

Refraction of light through a glass slab (lateral deciation through a glass slab)
(a) Introduction: Diagram shows a section ABCD of a glass slab taken by a horizontal plane. The slab has thickness t.
(b) Description:
PQ is the incident ray
QR is the refracted ray
RS is the emergent ray.
∠PQN₁ = i = angle of incidence
∠RQN₂ = r = angle of refraction
∠SRN₄ = e = i = angle of emergence
∠TQR = i – r – angle of deviation.
Emergent ray goes parallel to the incident ray.
TU = RV = d = lateral displacement suffered by the emergent ray.

(a) Definition: The perpendicular distance between the parallel emergent ray and the incident ray, is called lateral displacement suffered by the incident ray.
It is represented by the symbol d. It is measured in m or cm.
(b) Calculation: In ΔRQN₂,

Real and apparent thickness of a glass slab
(a) Introduction. Diagram shows a section ABCD of a glass slab taken by a horizontal plane. The slab has thickness t.
(b) Description. P is a point mark (object) at the bottom of the slab. A ray of light PQ from P is incident at the top at the point Q at an angle of incidence i and refracts along QR at an angle r. It appears to come from  P₁.P₁ is the virtual image of real object P formed on normal PSN.

(c)Calculation

This is an important relation. It is used for determination of refractive index of the material of the transparent glass slab.

Refractive Index of Prism Material, Glass Slab and Transparent Liquid

Refraction
(a) Introduction: When a ray of light travelling in a straight line in a transparent homogeneous medium with

certain velocity, enters another transparent medium in which it has different velocity, it bends at the boundary (interface) of two media and then travel again on a straight line in the other medium.
(b) Refraction: It is a phenomenon of bending of a ray of light at the boundary (interface) of two optical media when light ray is going from one optically medium to another.
The cause of refraction is the difference of speed of light from one medium to another.
Laws of refraction: There are two laws :
(i) Snells law. According to this law, the ratio of sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media from

(ii) The refracted ray (OB), incident ray (AO) and normal (N₁N₂) all lie in the same plane.

Refractive Index
(а) Definition: The ratio of velocity of light in first medium to its velocity in second medium, is called refractive index of second medium with respect to first medium. It is represented by the symbol p (mu) or n.
(b) Expression: Let light have velocity v₁ in first medium (medium a) and v₂ in second medium (medium b).

(c) Unit: As refractive index is ratio of two similar quantities, it has no unit and dimensions.

Absolute Refractive Index
(а) Definition. The ratio of velocity of light in air (strictly vacuum) to its velocity in a medium, is called absolute refractive index of the medium.
(b) Expression. Light has velocity c in air (strictly vacuum). If velocity of light in the medium be v, then absolute refractive index of the medium,
n_m = c/v

Prism
A prism is a piece of a transparent material bounded by three rectangular surfaces forming a triangle. One surface (which may be opaque or transparent) is called base. Other two surfaces a Prism are transparent and are called refracting surfaces. The line along which the refracting surfaces meet, is called the edge of the prism. The angle between the two refracting surfaces, is called the angle of prism or refracting angle of prism

Refraction of Light Through
Diagram shows section ABC of a prism taken by a vertical plane, perpendicular to the edge. BC is the base of the prism and AB and AC are its two refracting surfaces.
RQ is the incident ray.
QS is the refracted ray.
ST is the emergent ray.
∠RQN₁ = i = angle of incidence

Angle of Minimum Deviation
(a) Definition. The minimum value of angle of deviation, is called angle of minimum deviation. It is represented by the symbol D_m.
(b) Explanation. For same angle of deviation CD) there are two values of angle of incidence. One value equals i and other value equals ‘e’ (Graph between i and D).
As angle i is increased from a small value, e decreases from large value and angle of deviation decreases. When angle of deviation is minimum (D_m ), then, i and e becomes equal.

Physics Lab ManualNCERT Solutions Class 12 Physics Sample Papers

To find the focal length of a concave lens using a convex lens

Physics Lab ManualNCERT Solutions Class 12 Physics Sample Papers

Aim
To find the focal length of a concave lens using a convex lens.

Apparatus
An optical bench with four upright (two fixed uprights in middle, two outer uprights with lateral movement), a convex lens (less focal length), a concave lens (more focal length), two lens holders, two optical needles (one thin, one thick), a knitting needle and a half metre  scale.

A Short Description about the Arrangement
As a concave lens always forms a virtual image, its focal length can not be found directly as for a convex lens. For this purpose, indirect method is used, as described below.
An object needle O is placed on one side of a convex lens L₁ and its real inverted image I is located (by image needle) on the other side as shown in ray diagram.
The concave lens L₂ is placed between convex lens L₁ and image needle I. The concave lens diverges the rays and the image is now formed at I’ as shown in ray diagram.
For concave lens, I is the virtual object and I’ is the real image. Hence, O₂I = u and O₂I’ = v.
Focal length can be calculated, using lens formula

Theory

Ray diagram

Procedure
To determine rough focal length of convex lens

1. Mount the convex lens in lens holder.
2. Go out in the open and face the lens towards distant tree or building.
3. Obtain the image of the tree or the building on a white painted wall (screen) and move the lens forward and backward to get a sharp image on the wall.
4. Measure the distance between the lens and the wall (screen). This will be equal to the rough focal length of the mirror.
   To set the convex lens
5. Follow steps 2 to 4 of Experiment 2 To set the object needle
6. Follow steps 5 to 8 of Experiment 2 To set the image needle at I
7. Follow steps 21 to 27 of Experiment 2 To set the concave lens
8. Clamp the holder with concave lens on fixed upright on the I side of the convex lens.
9. Fix this upright at some distance away from the convex lens.
10. Set the concave lens surface in same manner as convex lens surface with principal axes of the lenses coinciding.
    To set the image needle at I’
11. Repeat steps 4 and 5 of the experiment.
    To get more observations
12. Follow steps 29, 30 and 31 of Experiment 2.

Observations

Calculations
1. Find difference of positions of  L₂ and I and write it as observed u in column 3a.
2. Find difference of positions of L₂ and I’ and write it as observed v in column 36.
3. Apply index correction and write corrected values of u and v in columns 4a and 46.
4. Calculate f = uv/u-v and write in column 5.
5. Take mean of different values of as recorded in column 5.

Result
The focal length of the given concave lens = -……cm

Precautions

1. Focal length of the convex lens should be less than the focal length of concave lens so that the combination is convex.
2. The lenses must be clean. .
3. Other precautions are same as given in Experiment 3.

Viva Voce

Question. 1. Define a spherical lens.
Answer. Read Art. 8.01 (a).

Question.2. Describe different types of lenses.
Answer. Read Art. 8.01 (b).

Question.3. Describe different types of convex lenses.
Answer. Read Art. 8.01 (c).

Question.4. Describe different types of concave lenses.
Answer. Read Art. 8.01 (d).

Question.5. Define different terms associated with spherical lenses.
Answer. Read Art. 8.02 (1-7).

Question.6. Mention three special rays.
Answer. Read Art. 8.03.

Question.7. Define sign convention.
Answer. Read Art. 8.04 (a).

Question.8. Give rules of sign convention.
Answer. Read Art. 8.04 (b).

Question. 9. Give facts obtained from sign convention.
Answer. Read Art. 8.04 (c).

Question.10. Define and give lens formula.
Answer. Read Art. 8.05.

Question.11. Describe various assumptions made in derivation of lens formula.
Answer. Read Art. 8.06.

Question.12. Give position, nature and size of image when object is put in different positions in front of a convex lens.
Answer. Read Art. 8.07.

Question.13. Define power of a lens. Give its unit and sign.
Answer. Read Art. 8.08.

Question.14. Define a lens combination. Give expression for. its focal length and power.
Answer. Read Art. 8.09.

Question.15. Define chromatic aberration.
Answer. Read Art. 8.10 (a).

Question.16. Describe the difference between the images formed by a convex and a concave lens. .
Answer. A concave lens always forms a virtual, erect and diminished image. Image formed by a convex lens is generally real and inverted and on bringing the object near the lens the size of image goes on increasing. However, when the object is placed in front of a convex lens between its optical centre and principal focus, the image formed is virtual, erect and magnified.

Question.17. Which convex lens has more focal length, thick or thin?
Answer. A thin convex lens has more focal length. ^ ..

Question.18. Can you find rough focal length of a concave lens?
Answer. No, because it does not form a real image to be obtained on a screen.

Question.19. What is the type of the eye lens?
Answer. The eye lens is convex.

Question.20. What are the practical uses of lenses?
Answer. Lenses are used in spectacles, microscopes, telescopes and other optical instruments.

Question.21. How can a convex lens be used as a magnifier?
Answer. For this purpose the lens is put very close to the eye in between the eye and the object to be magnified.

Question. 22. How will you distinguish between a glass slab, a convex lens and a concave lens without touching it?
Answer. The glass piece is put over a printed page and the virtual image of the printed matter is seen. The magnification of the image is judged.
If the image has same size as the object, the glass piece is a glass slab.
If the image is magnified, the glass piece is a convex lens.
If the image is diminished, the glass piece is a concave lens.

Question. 23. Define optical centre of a len.
Answer. It is a fixed point inside the lens on its principal axis, through which fight rays passing undeviated.

Question.24. What is the principal axis of a lens?
Answer. The straight fine passing through the centres of curvature of the curved surfaces of the lens is called the principal axis of the lens.

Question.25. What is the principal focus of a lens?
Answer. It is fixed point on the principal axis of a lens where a beam of fight incident parallel to its principal axis converges or appears to diverge after passing through the convex lens or concave lens.

Question. 26. What is the focal length of a lens?
Answer. It is the distance between optical centre and principal focus of a lens. Its S.I. unit is metre.

Question.27. Define S.I unit of power.
Answer. The Dioptre is the S.I. unit of power. One dipotre is the power of lens whose focal length is one metre.

Question. 28. What are the sign for the power of a convex lens and concave lens?
Answer. The power of a convex lens is positive since its focal length is positive while the power of a concave lens is negative since its focal lens is negative.

Question. 29. What is a lens maker formula?
Answer. It is relation between focal length, radii of curvature, refractive index of material of lens and refractive index of surroundings.

Question.30. What are the factors affecting the power of lens?
Answer.

1. Refractive index of lens material
2. Refractive index of surroundings i.e., change of medium
3. Radii of curvature
4. Wavelength of light
5. Thickness of lens.

Question.31. How the power of lens charge w.r.t. the two surrounding medium?
Answer. The power of a lens is maximum for vacuum or air and it decreases with increase in two refractive index of medium.

Question.32. How the power of lens charge w.r.t. to wavelength of light?
Answer. The power of a lens is different for different colour of light. The power of a lens is maximum of violet and minimum for red colour light.

Question. 33. Does power depend upon aperature of a lens?
Answer. No.

Question.34. Under what condition, the nature of lens change?
Answer. The refractive index of surrounding medium is greater them that of material of lens. The convex lens act as concave lens and vice-versa.

Question. 35. Under what condition, a lens does not show the refraction.
Answer.When refractive index of surrounding medium is equal to refractive index of material of lens.

Question.36. Why goggles (Sun glasses) have zero power?
Answer. The surfaces are curved in same direction and of same radius

Question. 37. What type of lens is an air bubble inside water?  
Answer. Concave lens.

Question.38.Define refractive index.
Answer.It is the property of a transparent medium which resist the propagation of light in that medium. It is measured in term of speed of light in a medium w.r.t. speed of light in vacuum.

Question.39.What is relative refractive index?
Answer.Relative refractive index of medium 2 w.r.t. medium 1 is the ratio of the speed of light in medium 1 to the speed of light in medium 2

It does not have emit and dimensions.

Question.40.What is absolute refractive index?
Answer. Absolute refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium.

Question.41.Is the absolute refractive can be less than unit?
Answer. No.

Question.42.What is the power of combination of a convex and concave lens of the same focal length?
Answer. Zero.

Question.43.Why is the rough focal length of concave lens not determine?
Answer. It makes virtual image for all positions of objects.

Question.44.How chromatic aberration can be minimized?
Answer. It can be minimized by taking thin and small aperature lens.

To Find the Focal Length of a Convex Lens by Plotting Graphs Between U and V or Between 1/u and 1/v

Aim
To find, the focal length of a convex lens by plotting graphs between u and v or between 1/u and 1/v.

Apparatus
An optical bench with three uprights (central upright fixed, two outer uprights with lateral movement), a convex lens with lens holder, two optical needles, (one thin, one thick) a knitting needle and a half metre scale.

Theory
The relation between u, v and f for a convex lens is

where,
f = focal length of convex lens
u = distance of object needle from optical centre of the lens
v = distance of image needle from optical centre of the lens.
Note. According to sign-convention, u has negative value and v has positive value. Hence, f comes positive.

Ray diagram

Procedure
To determine rough focal length

1. Mount the concave mirror in mirror holder.
2. Go out in the open and face the mirror towards distant tree or building.
3. Obtain the image of the tree or the building on a white painted wall (screen) and move the mirror forward and backward to get a sharp image on the wall.
4. Measure the distance between the mirror and the wall (screen). This will be equal to the rough focal length of the mirror.
   To set the lens
5. Clamp the holder with lens in a fixed upright and keep the upright at 50 cm mark.
6. Adjust the lens such that its surface is vertical and perpendicular to the length of the optical bench.
7. Keep the upright fixed in this position throughout.
   To set the object needle
8. Take the thin optical needle as object needle (O). Mount it in outer laterally move¬able upright near zero end.
9. Move the object needle upright and clamp it at a distance (in full cms) nearly 1.5 times the obtained rough focal length of the lens.
10. Adjust height of the object needle to make its tip lie on horizontal line through the optical centre of the lens.
11. Note the position of the index mark on the base of the object needle upright.
    To set the image needle
12. With left eye closed, see with the right open eye from the other end of the optical bench. An inverted and enlarged image of the object needle will be seen. Tip of the image must lie in the middle of the lens.
13. Mount the thick optical needle (image needle) in the fourth upright near the other end of the optical bench.
14. Adjust the height of the image needle so that its tip is seen in line with the tip of the image when seen with right open eye.
15. Move the eye towards right. The tips will get separated. The image tip and the image needle tip have parallax.
16. Remove the parallax tip to tip.
17. Note the position of the index mark on base of the image needle upright.
18. Record the position of the index marks on the base of upright of the lens, the object needle and the image needle in the table against observation 2.
    To determine index correction
19. Find the index correction for distance between optical centre of lens and tip of the object needle and also for distance between optical centre of lens and tip of the image needle as described.
    To get more observations
20. Move object needle upright towards mirror in steps of 1 cm to get observation 2 and 1. Repeat the experiment.
21. Move object needle upright away from mirror (from position of observation 2) in steps of 1 cm to get observations 4, 5 and 6. Repeat the experiment.
22. Record all the observations as given ahead.
    (Note. Same as in Experiment 1).

Observations
Rough focal length of the given convex lens = …….cm
Actual length of the knitting needle x=…….cm
Observed distance between the object needle and the lens
when knitting needle is placed between them y =…….cm
Observed distance between the image needle and the
lens when knitting needle is placed between them z =…….cm
Index correction for the object distance u, x -y =…….cm
Index correction for the image distance v, x-z =…….cm

Calculations
Calculations of focal length by graphical methods:
(i) u-v Graph. Select a suitable but the same scale to represent u along X’-axis and v along Y-axis. According to sign conventions, in this case, u is negative and v is positive. Plot the various points for different sets of values of u and v from observation table second quadrant. The graph comes out to be a rectangular hyperbola as shown in graph between u and v.
Draw a line OA making an angle of 45° with either axis (i.e., bisecting ∠YOX’) and meeting the curve at point A. Draw AB and AC perpendicular on X’- and Y-axes, respectively.
The values of u and v will be same for point A. So the coordinates of point A must

Explanation
Same as for concave mirror:
(iii) Another u-v Graph. Select a suitable but the same scale to represent u along
X’-axis and v along Y-axis. Mark the points at distances u₁, u₂, u₃,…… etc. along the OX’-axis
and the corresponding points at distances v₁, v₂, v₃,…… etc. along OY- axis for different sets of observations from the table.
Draw straight lines joining u₁ with v₁; u₂ with v₂; u₃ with v₃;……. etc. These lines will intersect at point K as shown in the following graph.
Draw KL and KM perpendiculars on X’- and Y-axes, respectively

Explanation
Same as for concave mirror:
Note. It will be better to choose any four suitable sets of (a, v) from the observation table. All the six sets of observations may complicate the graph.

Result
The focal length of the given convex lens as determined from

Precautions

1. Tips of the object and image needles should lie at the same height as the centre of the lens.
2. Parallax should be removed from tip to tip by keeping eye at a distance at least 30 cm away from the needle.
3. The object needle should be placed at such a distance that only real, inverted image of it is formed.
4. Index correction for u and v should be applied.

Sources of error

1. The uprights may not be the vertical.
2. Parallax removal may not be perfect.

Physics Lab ManualNCERT Solutions Class 12 Physics Sample Papers

Focal Length of Spherical Lenses

Physics Lab ManualNCERT Solutions Class 12 Physics Sample Papers

Spherical lens 
(а) Definition: A piece of a transparent medium bounded by atleast one spherical surface, is called a spherical lens.
(b) Types: There are two types of spherical lenses.

1. Convex or Converging Lenses: These are thick in the middle and thin at the edges.
2. Concave or Diverging Lenses: These are thin in the middle and thick at the edges.

(c) Different types of convex lenses: The three types of convex lenses are

1. double convex
2. plano-convex
3. concavo-convex

(d) Different types of concave lenses: The three types of concave lenses are

1. double concave
2. plano-concave
3. convexo-concave
   

Terms associated with spherical lenses 

1. Aperture: The diameter of the circular edge of the lens, is called the aperture of the lens.
   In diagram  AB is the aperture of the lens.
2. Principal axis: The straight line passing through the two centres of curvature of the two spherical surfaces of the lens (or through one centre of curvature of one spherical surface and normal to the other plane surface), is called the principal axis of the lens.
   
3. Optical centre: It is a point on the principal axis of the lens, such that a ray of light passing through it goes undeviated.
   In diagram, O is the optical centre of the lens.
4. First principal focus: It is a point on the principal axis of the lens, such that the rays actually diverging from it (in case of a convex lens) or appearing to be going towards it (in case of a concave lens), after refraction from the lens, go parallel to the principal axis.
   In diagram,F₁ is the first principal focus of the lens. (For object at F₁ image at infinity).
5. Second principal focus: It is a point on the principal axis of the lens, such that the rays incident on the lens parallel to the principal axis after refraction from the lens, actually meet at this point (in case of a convex lens) or appear to come from it (in case of a concave lens).
   In diagram, F₂ is the second principal focus of the lens (For image at F₂ object at infinity).
6. Focal length: The distance between the optical centre of the lens and the principal focus (first or second) of the lens, is called focal length of the lens. It is represented by the symbol f. In diagram,OF₁ = OF₂ = f.
7. Principal section: A section of the lens cut by a plane passing through the principal focus and optical centre of the lens, is called principal section of the lens. It contains the principal axis.
   In diagram, the shaded portion is the principal section of the lens cut by the plane of the book page.

Three special rays
The special rays are :

1. Incident on the lens parallel to principal axis. After refraction from the lens, it actually passes through second principal focus F₂ (in case of a convex lens) or appears to come from the second principal focus F₂ (in case of a concave lens).
   
2. Incident on the lens through first principal focus F₁ (in case of a convex lens) or in direction of first principal focus F₁ (in case of a concave lens).
   After refraction from the lens, it goes parallel to the principal axis.
3. Incident on the lens in direction of optical centre. It passes undeviated through the lens.

Sign convention 
(a) Definition: It is a convention, which fixes the sign of different distances measured. The sign convention followed is the New Cartesian sign convention.
(b) Rules: It gives following rules:

1. All distances are measured from the optical centre of the lens (along the principal axis).
2. The distances measured in the same direction as the direction of incident light, are taken as positive.
3. The distances measured opposite to the direction of incident light, are taken as negative.
4. The distances measured above the principal axis are taken as positive but distances measured below the principal axis are taken as negative.
   

(c) Facts: According to above mentioned rules of sign convention,

1. Focal length for a convex lens is taken positive and the same for concave lens is taken negative.
2. The distance of an object is always negative.
3. The distance for real image is positive, while that for a virtual image is negative.
4. The size of object is positive and size of real image is negative while size of virtual image is positive.

Lens formula
The equation relating the object distance (u), the image distance (u) and the lens focal length (f), is called lens formula. It is also called Gaussian formula.

Assumptions made
Following assumptions are made in derivation of the lens formula.

1. The lens is thin.
2. The lens has a small aperture.
3. The point object lies on to the principal axis and placed perpendicular.
4. The incident rays make small angles with the lens surface or the principal axis.

Position, nature and size of image when object is put in different position in front of a convex lens 
                                                                        It is described below in tabular form.

Power of a lens 
(a) Definition: It is the capacity or ability of a lens to deviate (converge or diverge) the path of rays passing through it. A lens producing more converging or more diverging is said to have more power and vice-versa.
It is represented by the symbol P.
(b) Relation with focal length: A lens of less focal length produces more converging or diverging rays and is said to have more power.

(c) Unit: Unit of power is dioptre (D). One dioptre is the power of a lens of focal length 1 metre.

(d) Sign: A converging lens has positive focal length and positive power.
A diverging lens has negative focal length and negative power.

Lens combination 
(a) Definition: Two or more thin lenses, placed in contact together to have a common principal axis, form a lens combination.
(b) Focal length: If f₁, f₂,….., f_n be the focal length of individual lens and F be the focal
length of the combination.

Note: The lenses forming the combination must be thin to have their optical centres coinciding at one point to represent optical centre of the combination.
(c) Power: If P₁, P₂,….., P_n be the power of individual lenses and P be the power of the
combination.

(d) Magnification: If m₁, m₂,….., m_n are the magnification of individual lenses and m is the equivalent magnification of the combination then,

Chromatic aberration of a lens 
(a) Definition: The defect or drawback of a lens due to which it makes a coloured image of an object illuminated with white light, is called chromatic aberration. It is due to dispersion of white light by lens (just like a prism does).
(b) Remedy: It is removed by combining a convex and a concave lens of suitable focal length and material.
The combination of two lenses is called an achromatic combination (achromic doublet).