Image Formation In Convex Lens

MATERIALS REQUIRED

A thin convex lens, a lens holder a piece of a semi-transparent sheet act as screen fixed to a stand with the centred mark; a small candle end stand for candle with centred mark and a meter scale (or a ruler)

THEORY

The light ray when refracted through a thin convex lens follow the law of refractions.

The formation of an image by lenses can be described using the new cartesian sign convention.

The new cartesian sign convention can be summarised as below:

(i) The object is always placed to the left of the lens.

(ii) All distances parallel to the principal axis are measured from the optical centre of the lens.

(iii) All distances measured to the right of the origin are taken as positive while those measures to the left of original taken as negative.

(iv) Distance measured perpendicular to and above the principal axis are taken as positive.

(v) Distances measured perpendicular to and below the principal axis are taken as negative.

The position, nature and size of the image of an object formed by s thin convex lens depend on the distance between the object and the optical centre and size of the object.

PROCEDURE

1. Place the semi-transparent paper screen in a vertical position fitted to a stand on the right-hand side of the convex lens.

2. Place a thin convex lens vertically on the lens holder.

3. Place the candle in a centred mark stand on the optical bench.

4. Place the lighted candle stand at a distance beyond R(2F₁) vertically in the front of a thin convex lens.

5. Adjust the height of the centre of the convex lens to be equal to the height of the flame of the candle as shown below.

6. Obtain a sharp image of the candle flame on the screen

7. Using measuring scale, record the position of lens and screen in the observation table.

8. Repeat the experiment by placing the lighted candle at a distance as given below:

(i) equal to 2F

(ii) less than 2F but more than F.

9. Find the distance between the optical centre of the lens and candle flame (object) to be x and corresponding image distance between the optical centre O of the lens and the screen be y.

OBSERVATIONS AND CALCULATIONS

The approximate focal length of the thin convex lens, F = 10 cm

The height of the candle flame, h = 2 cm.

RESULT

When the object is moved from infinity towards the optical centre of the convex lens.

(a) the image distance increases gradually.

(b) the size of the image also tosses gradually.

1. The base of the candle stand, convex lens and the screen must be parallel to the measuring scale.

2. The lens should be held vertically inside the lens holder.

3. Flame of the candle must be uniform and continuous throughout the experiment.

MATERIALS REQUIRED

A drawing board, sheets of white paper, measuring scale, protractor and drawing pins or adhesive tape.

THEORY

The light ray when refracted through a convex lens obey the laws of refraction. The formation of images by a convex lens can be studied by drawing ray diagrams. using the new cartesian sign convention as given in the figure.

The new cartesian sign convention can be summarised as below:

(i) The object is always placed to the left of the lens.

(ii) All distances parallel to the principal axis are measured from the optical centre of the lens.

(iii) All distances measured to the right of the origin are taken as positive while those measured to the left of original taken as negative.

(iv) Distance measured perpendicular to and above the principal axis are taken as positive.

(v) Distances measured perpendicular to and below the principal axis are taken as negative.

Daw ray diagrams are forming images by a convex lens for various positions of the object.

The position of the object may be

(a) beyond 2F₁

(b) at 2F₁

(c) between F₁ and 2F₁,

(d) at F₁,

(e) between focus (F₁) and optical centre (O) of the convex lens.

PROCEDURE

1. Place a white sheet of paper on a drawing board using pins and cello tape.

2. Draw a thin line 20 cm in length in the middle of the paper using a sharp pencil and a meter scale. Name it as XX’.

3. Mark a point ‘O’ at the centre of this line. Draw a perpendicular line of equal height at the point O as the optical centre above and below XX’. Name it L₁L₂.

4. Mark points F₁ and F₂ on the line ‘XX on either side of the lens L₁L₂ such that OF₁ = OF₂ where F₁ and F₂ are the two principal foci of the lens.

5. Also, mark points R₁ and R₂ on the line XX’ such that O(R₁) = 2(OF₁) and O(R₂)= 2 (OF₂).

6. Draw the object AB of suitable height ‘h₁’ at a very far distance from the lens considered to be placed at infinity.

7. Draw thin lines parallel to the principal axis such as CD, GH, PQ and RS incident on the surface of the convex lens.

8. Draw the emergent rays on the other side of the lens such as DF HF QF and SF through the convex lens and intersect at the first focus F.

9. Record the result in an observation table.

10. Fix second white sheet of paper on the drawing board.

11. Repeat the steps (2) to (6).

12. Draw an object AB of suitable height beyond 2F₁ as shown.

13. Draw a ray of light AE parallel to the principal axis F₁OF₂ incident on the surface of the convex lens at point E.

14. Draw another ray AO through the optical centre O of a convex lens and extend it to another side of the lens as OA.’

15. On the other side of the convex lens, draw the ray EF₂ passing through the focus F₂ and intersecting the ray OA’ at A as shown in the figure, forming an image B’A.

16. Measure the height of the image A’B’(h₂).

17. We observe from the figure that the image formed is real, inverted, smaller in size and in between F₂ and 2F₂.

18. Record the reading in the table

19. Repeat the above steps similar to the previous case. Draw ray diagrams for other positions of the object as shown in the

20. Measure the height of the object AB (h₁) and height of image A’B’(h₂) respective in all cases (c) to (f) as listed in step 20. Record them in the observation table.

21. Note down nature. Relative size and position of the image formed by the convex lens for the various positions of the object.

22. Tabulate your observations in the observation table.

OBSERVATION AND CALCULATION

RESULT

PRECAUTIONS

1. The convex lens should be thin and have a small aperture and should be without any scratches to get the distinct image of the object.

2. The lens should be placed completely vertically inside the lens holder.

3. The ray diagram should be drawn with a sharp pencil.

A convex lens is used for focusing of light rays at a specific point whereas a concave lens is a diverging lens diverges the light rays

The size of the image increases gradually when it is brought close to the optical center. Example, when a candle is placed between focus “F” and optical centre “O”, then a very enlarged image is formed as shown below:

Real and the inverted image are formed. The image formation diagram is shown here:

Sharp and distant images cannot be obtained accurately due the scratches on the lens.

The virtual image is always erect and enlarged.

Between focus and optical center of the lens.

It depends on the position of an object from the lens.

An equiconvex lens has the same radius of curvature on both surfaces. If the drawn lens is not equiconvex, then the condition OF₁ = OF₂ will not hold.

We draw two rays because:

1. For the sake of clarity of ray diagram.

2. To know their direction easily after refraction from the lens.

The frequency of the ray of light remains constant during refraction. When light changes it medium, then there is no loss in energy of the wave. Since, there is no loss in energy hence, no change in frequency as well. The frequency remains constant.

Nature of the image formed by a thin convex lens for a distant object is real, inverted and highly diminished. It is formed at the focus of a convex lens.

If the letter of the printed page appears enlarged then it is a convex lens , but if it appears diminished than it is a concave lens.

With the flickering flame we can not get a sharp and bright image of our object.

To get the sharp and distinct image of the candle flame, it should be better this experiment in the dark.

The object should be placed between F₁ and 2F₁ in front of the convex lens so that the obtained image is real, inverted, magnified and formed beyond the center of curvature.

The ray diagram is shown below: