Question

What is the focal length of the convex lens used? Give reason to justify your answer.

Answer 1

(a) Focal Length of the Convex Lens:
We will calculate the focal length using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where:
- \( f \) is the focal length,
- \( v \) is the image distance,
- \( u \) is the object distance.
We will consider two observations to calculate the focal length. Observation 1: Object distance \( u = -60 \, \text{cm}, \, v = +20 \, \text{cm} \) Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{20} - \frac{1}{-60} \] \[ \frac{1}{f} = \frac{1}{20} + \frac{1}{60} = \frac{3}{60} = \frac{1}{20} \] Thus, the focal length is: \[ f = 20 \, \text{cm} \] Observation 2: Object distance \( u = -40 \, \text{cm}, \, v = +24 \, \text{cm} \) Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{24} - \frac{1}{-40} \] \[ \frac{1}{f} = \frac{1}{24} + \frac{1}{40} = \frac{5}{120} = \frac{1}{24} \] Thus, the focal length is: \[ f = 24 \, \text{cm} \] The average of the focal lengths from the two observations is: \[ f_{\text{avg}} = \frac{20 + 24}{2} = 22 \, \text{cm} \] Thus, the focal length of the convex lens is approximately \( \boxed{22 \, \text{cm}} \).

Answer 2

Let us analyze the data provided:

The object distances are all negative (since the object is placed on the left side of the lens), and the image distances are positive, indicating the formation of a real and inverted image. We observe the following trend: As the object distance becomes smaller (i.e., as the object approaches the lens), the image distance increases. This is the expected behavior for a convex lens, where the image distance should increase as the object distance decreases. The pattern follows the general trend, except for the following observation:
- When the object is at a distance of -24 cm, the image distance is +40 cm.
- However, when the object is at -20 cm, the image distance increases to +60 cm, which is expected. Thus, the set where the object distance is -24 cm and the image distance is +40 cm does not align with the general rate of change between object and image distances. Conclusion: The observation set with the object at -24 cm and the image at +40 cm is not correct because it does not follow the expected pattern of increasing image distance with decreasing object distance.

Answer 3

A ray diagram for a convex lens will show how light rays from the object (candle flame) pass through the lens and form an image on the screen. In this case, for object distances such as -60 cm and -40 cm, the rays converge on the other side of the lens to form a real and inverted image. A ray diagram for any set of observations, such as when the object is placed at a distance of -60 cm from the lens, is as follows:
1. Draw a convex lens in the center.
2. Mark the focal point (F) on both sides of the lens.
3. Draw the object (the candle flame) to the left of the lens.
4. Draw two light rays from the object: one parallel to the principal axis, which refracts through the focal point on the opposite side, and the other passing through the center of the lens without bending.
5. The point where the refracted rays meet is where the image is formed on the screen.