Image Distance for Varying Object Distances

Lens Diagram

The lens is a transparent material bounded by two surfaces in which at least one of the surfaces is spherical. It has a principal axis, optical centre, aperture, centre of curvature of lens and principal focus. The two types of lenses are the convex lens and the concave lens. The images formed by these lenses can be real or virtual, depending on various conditions. In this article, we will perform an experiment to observe image distance for different object distances with ray diagrams using a convex lens.


Theory

Convex Lens: A lens which is thin at the edges and thick at the centre is known as a convex lens. This lens converges the light beam incident on it; hence, it is popularly known as a converging lens. 

Lens Formula: It is a formula that describes a relationship between object distance and image distance along with focal length. The mathematical representation of this formula is:

1/f= (1/v) - (1/u)

Where v is the distance of the image from the optical centre, f is the focal length of the lens, and u is the distance of the object from the optical centre.


Materials Required

The following materials are essential for the image formation by convex lens experiment.

  • A convex lens with short focal length (12-20 cm)

  • Optical bench

  • A candle

  • A needle

  • Measuring Scale


Procedure

  1. Place a lens holder and fix the thin convex lens on it. 

  2. Fix the screen on another side of the convex lens and adjust the candle to get an inverted image of the fixed screen, which is clear and sharp. Measure the distance of the candle to get the rough focal length of the lens.

  3. Mark the fixed location of the convex lens as ‘O’.

  4. Now, mark the point F on both sides of the convex lens after calculating the focal length in the first step.

  5. Mark the point 2F on both sides of the convex lens, which is twice the focal length of the convex lens.

  6. Place the candle on the table on the optical bench at beyond 2F distance. Make sure that the height of the flame of the candle must be equal to the centre of the lens by adjusting its height.

  7. Now, adjust the position of the screen to locate a sharp image of the candle flame from another side of the convex lens.

  8. Place the lighted candle at 2F point to record the observations.

  9. Now, shift the object between F and 2F and record the observations. After that, place the object at point F to record the observations.

  10. Place the object between F and O and then record the observations.

  11. Finally, draw the ray diagram for the various positions of the object at which we have recorded the observations.

(Image to be added soon)

The above image shows the ray diagram for different positions of object and image while recording observations.   

Observations and Calculations 

Sl No

Position of the optical center O of the lens ‘l’ cm

Position of candle ‘a’ cm

Position of screen ‘s’ cm

Distance between lens and candle (object distance) 

u =  a – l (cm)

Distance between object and screen (image distance)

v = s – l (cm)

Focal length (f)

1

50

30

70

-20

20

10 cm

2

50

35

80

-15

30

10 cm

3

50

20

65

-30

15

10 cm

4

50

40

No image obtained on the screen

-10

Infinity


5

50

45

No image obtained on the screen

-5

Virtual image obtained and cannot be taken on the screen



Case 1: 1/f= (1/v)- (1/u) ⟹ 1/f = 120 - (1/-20) = 2/20 =  1/10  ⟹ f = 10 cm

Case 2: 1/f= (1/v)- (1/u) ⟹ 1/f = 1/30 - (1/-15) = 3/30 =  1/10  ⟹ f = 10 cm

Case 3: 1/f= (1/v)- (1/u) ⟹ 1/f = 1/15 - (1/-30) = 3/30 =  1/10  ⟹ f = 10 cm

Result

Sl No. 

Position of the object

Position of the image

 The relative size of the image

Nature of the image

1

At 2F1

At 2F2

Same size

Real and inverted

2

Between F1 and 2F1

Beyond 2F2

Enlarged

Real and inverted

3

Beyond 2F1

Between F2 and 2F2

Diminished

Real and inverted

4

At Focus F1

At infinity

Infinitely large or highly enlarged

Real and inverted

5

Between Focus F1 and optical centre O

On the same side of the lens as an object

Enlarged

Virtual and erect

6

At infinity

At focus F2

Highly diminished, point-sized

Real and inverted

FAQ (Frequently Asked Questions)

1. What Are The Precautions To Be Taken While Performing Image Formation By The Convex Lens Experiment?

First of all, it is essential to use a convex lens with a focal length of 15-20 cm for the experiment. Moreover, the observer must use a thin convex lens of a small aperture. The observer must perform the analysis in calm air to prevent the flickering of the candle during the process. To get a sharp and distinct image of the candle image, make sure to perform this process in a dark room. The object and image screen, as well as the optical bench, must not be shaky.

2. What is The Power Of The Lens?

In simple words, the ability of a lens to bend the light rays is its power. It means the higher the power of a lens, the more easily it can refract light passing through it. The concave lens diverges the light away from the principal axis while the convex lens converges the light rays to the principal axis. The reciprocal of the focal length of the lens after converting it in meters is its power. It is important to note that the power of the convex lens is positive, whereas the power of the concave lens is negative. Its SI unit is Dioptre denoted by ‘D’.