A student placed a candle flame at different distances from a convex lens and focused its image on a screen. He recorded his observation in tabular form as given below:
Question: 1
What is the focal length of the convex lens used? Give reason to justify your answer.
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The focal length of a convex lens is positive and can be calculated using the lens formula with object and image distances.
(a) Focal Length of the Convex Lens:
The focal length is calculated 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.
Two observations are used to calculate the focal length.
Observation 1: Object distance \( u = -60 \, \text{cm}, \, v = +20 \, \text{cm} \)
Applying the lens formula:
\[\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{20} - \frac{1}{-60}\]
\[\frac{1}{f} = \frac{1}{20} + \frac{1}{60} = \frac{3}{60} = \frac{1}{20}\]
Therefore, the focal length is:
\[f = 20 \, \text{cm}\]
Observation 2: Object distance \( u = -40 \, \text{cm}, \, v = +24 \, \text{cm} \)
Applying the lens formula:
\[\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{24} - \frac{1}{-40}\]
\[\frac{1}{f} = \frac{1}{24} + \frac{1}{40} = \frac{5}{120} = \frac{1}{24}\]
Therefore, the focal length is:
\[f = 24 \, \text{cm}\]
The average of the focal lengths from both observations is:
\[f_{\text{avg}} = \frac{20 + 24}{2} = 22 \, \text{cm}\]
Thus, the focal length of the convex lens is approximately \( \boxed{22 \, \text{cm}} \).
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Question: 2
Which one of the sets of observations is not correct and why?
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In convex lenses, as the object distance decreases, the image distance increases for real and inverted images.
Data analysis:Object distances are negative, and image distances are positive, indicating a real, inverted image.As the object distance decreases, the image distance increases, consistent with a convex lens.Exception: - Object distance: -24 cm, image distance: +40 cm. - Object distance: -20 cm, image distance: +60 cm.The data point (-24 cm, +40 cm) deviates from the observed trend. Conclusion: The observation with an object at -24 cm and an image at +40 cm is inaccurate as it contradicts the expected relationship between object and image distances.
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Question: 3
Draw Ray Diagram to show Image Formation for any correct set of observation.
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In ray diagrams for convex lenses, parallel rays converge at the focal point on the opposite side of the lens, forming real and inverted images.
A convex lens ray diagram illustrates how light rays from an object (e.g., a candle flame) pass through the lens and create an image on a screen. For object distances like -60 cm and -40 cm, the rays converge on the opposite side of the lens, forming a real and inverted image.
To construct a ray diagram, such as when the object is -60 cm from the lens:
1. Draw a convex lens in the center.
2. Mark the focal point (F) on both sides of the lens.
3. Place the object (candle flame) to the left of the lens.
4. Draw two light rays from the object: one parallel to the principal axis, refracting through the focal point on the opposite side, and the other passing straight through the lens's center.
5. The intersection of the refracted rays indicates the image's location on the screen.
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