Let's break down the steps for conducting the experiment and solving the problem.

1. Measurements

Let's consider the following scenario:

• Object: A small toy of height $h_o = 10 \, \text{cm}$.
• Light Source: A torch placed at a fixed distance.
• Distance of the object from the light source (d1 and d2):
  • Close distance, $d_1 = 30 \, \text{cm}$.
  • Far distance, $d_2 = 60 \, \text{cm}$.

We will now place the object at $d_1$ and measure the height of the image ($h_1$), and then at $d_2$ and measure the height of the image ($h_2$).

2. Finding Proportion

The experiment is governed by the principle of similar triangles. The height of the image ($h_i$) and the distance of the object from the light source ($d$) are proportional. Mathematically, this can be written as:

$\frac{h_1}{h_2} = \frac{d_1}{d_2}$

Let's assume the measured heights of the images are:

• $h_1 = 20 \, \text{cm}$ when the object is at $d_1 = 30 \, \text{cm}$,
• $h_2 = 10 \, \text{cm}$ when the object is at $d_2 = 60 \, \text{cm}$.

Now, we can check the proportion:

$\frac{h_1}{h_2} = \frac{20}{10} = 2$ $\frac{d_1}{d_2} = \frac{30}{60} = 0.5$

Clearly, the heights are not in proportion with the distances. This suggests that some factor, like light dispersion or shadow distortion, might be affecting the results.

3. Reflection (Inference/Pattern)

From the calculations, we observe that the proportionality between the image height and the object distance isn't perfect. This could indicate that the light is not behaving like a point source, or other environmental factors, such as surface unevenness or light diffusion, are affecting the image.

For an ideal point light source and an object casting a sharp shadow, the image heights should follow a strict proportion based on the distances. The deviations here suggest non-ideal conditions in the experiment setup.

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Would you like to go deeper into this explanation or explore the effects of light diffusion?

5 Related Questions:

1. How does the size of the light source affect the proportion of the image height?
2. What happens if the object height is changed while keeping the distance constant?
3. How does the wall's surface texture affect the clarity and size of the image?
4. Can we calculate the angle of light spread based on the height measurements?
5. How would this experiment change if we used a laser instead of a torch?

Tip:

For more accurate results, try to make the light source as close to a point source as possible, such as using a small LED or focusing the light beam.