Observations:
- The student focused the image of a candle flame on a white screen using a convex lens.
- The student placed the flame at various distances from the lens.
- The student recorded his observations in a table.

Table:
| Distance of Candle Flame (cm) | Distance of Lens (cm) |
|------------------------------|----------------------|
| 45 | 40 |
| 40 | 20 |
| 35 | 14 |
| 30 | 10 |
| 25 | 8 |
| 20 | 6 |

Finding the Focal Length without Using Lens Formula:
To find the focal length of the lens without using the lens formula, we can make use of the observations recorded by the student and apply the concept of lens equation.

Step 1: Calculating the Object Distance:
To calculate the object distance, we subtract the distance of the lens from the distance of the candle flame for each observation.

- For the first observation: Object distance = 45 cm - 40 cm = 5 cm
- For the second observation: Object distance = 40 cm - 20 cm = 20 cm
- For the third observation: Object distance = 35 cm - 14 cm = 21 cm
- For the fourth observation: Object distance = 30 cm - 10 cm = 20 cm
- For the fifth observation: Object distance = 25 cm - 8 cm = 17 cm
- For the sixth observation: Object distance = 20 cm - 6 cm = 14 cm

Step 2: Calculating the Image Distance:
To calculate the image distance, we subtract the object distance from the distance of the lens for each observation.

- For the first observation: Image distance = 40 cm - 5 cm = 35 cm
- For the second observation: Image distance = 20 cm - 20 cm = 0 cm
- For the third observation: Image distance = 14 cm - 21 cm = -7 cm
- For the fourth observation: Image distance = 10 cm - 20 cm = -10 cm
- For the fifth observation: Image distance = 8 cm - 17 cm = -9 cm
- For the sixth observation: Image distance = 6 cm - 14 cm = -8 cm

Step 3: Calculating the Focal Length:
To calculate the focal length, we can use the formula:

1/focal length = 1/object distance + 1/image distance

- For the first observation: 1/focal length = 1/5 + 1/35 = 8/35
- For the second observation: 1/focal length = 1/20 + 1/0 (undefined)
- For the third observation: 1/focal length = 1/21 + 1/-7 (undefined)
- For the fourth observation: 1/focal length = 1/20 + 1/-10 (undefined)
- For the fifth observation: 1/focal length = 1/17 + 1/-9 (undefined)
- For the sixth observation: 1/focal length = 1/14 + 1/-8 (undefined)

Step 4: Finding the

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