 # 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.

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