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Given that the magnification is represented as \( \frac{v}{u} = \text{Image size} / \text{Object size} \), determine the size of the image if \( \frac{v}{u} = 10^{-1} \), \( 1.5 \times 10^{11} \), and \( 1.39 \times 10^9 \).

1. The diameter of the sun's image is \( 9.2 \times 10^{-4} \, \text{m} \).
2. The diameter of the sun's image is \( 9.2 \times 10^{-3} \, \text{m} \).
3. The diameter of the sun's image is \( 9.2 \times 10^{-2} \, \text{m} \).
4. The diameter of the sun's image is \( 9.2 \times 10^{-1} \, \text{m} \).

Correct answer: The diameter of the sun's image is \( 9.2 \times 10^{-4} \, \text{m} \).

Solution

The magnification formula relates the size of the image to the size of the object as \( \frac{v}{u} = \frac{\text{Size of image}}{\text{Size of object}} \). Substituting \( \frac{v}{u} = 10^{-1} \) and the size of the object as \( 1.39 \times 10^9 \), the size of the image is \( 10^{-1} \times 1.39 \times 10^9 = 1.39 \times 10^8 \). Dividing by \( 1.5 \times 10^{11} \), the diameter of the sun’s image is approximately \( 9.2 \times 10^{-4} \).

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