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A boy is trying to start a fire by focusing sunlighton a piece of paper using an equiconvex lens offocal length 10 cm. The diameter of the Sun is 1.39 ×109 m and its mean distance from the earthis 1.5 × 1011 m. What is the diameter of the Sun’simage on the paper? [2008]
- a)9.2 × 10–4 m
- b)6.5 × 10–4 m
- c)6.5 × 10–5 m
- d)12.4 × 10–4 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A boy is trying to start a fire by focusing sunlighton a piece of pape...
We have, 
or, Size of image = 
∴ Diameter of the sun’s image = 9.2 × 10–4 m.
Most Upvoted Answer
A boy is trying to start a fire by focusing sunlighton a piece of pape...
× 10^6 km and its distance from Earth is approximately 150 million km. Assuming the lens has a diameter of 5 cm, what is the minimum distance the paper should be placed from the lens to start a fire?
First, we need to convert the diameter of the Sun from kilometers to centimeters:
1.39 × 10^6 km = 1.39 × 10^9 cm
Next, we need to find the angle that the Sun subtends at the lens, using the formula:
θ = 2 tan^-1 (d/2f)
where d is the diameter of the Sun and f is the focal length of the lens. Substituting the values, we get:
θ = 2 tan^-1 (1.39 × 10^9 cm / 2 × 10 cm) = 78.5°
This means that the Sun will appear to cover an angle of 78.5 degrees when viewed through the lens.
Now, we need to find the distance from the lens where the image of the Sun will be formed. Using the thin lens formula:
1/f = 1/di + 1/do
where di is the image distance and do is the object distance. We can assume that the object distance is very large compared to the focal length of the lens, so we can approximate do as infinity. This gives:
1/f = 1/di
Solving for di, we get:
di = f = 10 cm
This means that the image of the Sun will be formed at a distance of 10 cm from the lens.
Finally, we need to find the distance between the lens and the paper. This will depend on the diameter of the lens and the size of the image of the Sun. Since the diameter of the lens is 5 cm, we can assume that the image of the Sun will be smaller than this. Let's assume that the image of the Sun has a diameter of 1 cm. Then, using similar triangles, we can find the distance between the lens and the paper:
(1 cm / 1.39 × 10^9 cm) = (x / 10 cm)
Solving for x, we get:
x = 1.39 × 10^-7 cm
This is a very small distance, but it makes sense since the lens is magnifying the image of the Sun by a large factor. Therefore, the minimum distance the paper should be placed from the lens to start a fire is approximately 1.39 × 10^-7 cm. However, it is important to note that this experiment should only be attempted with extreme caution and proper safety measures in place, as focusing sunlight can be very dangerous and can cause fires or eye damage.
First, we need to convert the diameter of the Sun from kilometers to centimeters:
1.39 × 10^6 km = 1.39 × 10^9 cm
Next, we need to find the angle that the Sun subtends at the lens, using the formula:
θ = 2 tan^-1 (d/2f)
where d is the diameter of the Sun and f is the focal length of the lens. Substituting the values, we get:
θ = 2 tan^-1 (1.39 × 10^9 cm / 2 × 10 cm) = 78.5°
This means that the Sun will appear to cover an angle of 78.5 degrees when viewed through the lens.
Now, we need to find the distance from the lens where the image of the Sun will be formed. Using the thin lens formula:
1/f = 1/di + 1/do
where di is the image distance and do is the object distance. We can assume that the object distance is very large compared to the focal length of the lens, so we can approximate do as infinity. This gives:
1/f = 1/di
Solving for di, we get:
di = f = 10 cm
This means that the image of the Sun will be formed at a distance of 10 cm from the lens.
Finally, we need to find the distance between the lens and the paper. This will depend on the diameter of the lens and the size of the image of the Sun. Since the diameter of the lens is 5 cm, we can assume that the image of the Sun will be smaller than this. Let's assume that the image of the Sun has a diameter of 1 cm. Then, using similar triangles, we can find the distance between the lens and the paper:
(1 cm / 1.39 × 10^9 cm) = (x / 10 cm)
Solving for x, we get:
x = 1.39 × 10^-7 cm
This is a very small distance, but it makes sense since the lens is magnifying the image of the Sun by a large factor. Therefore, the minimum distance the paper should be placed from the lens to start a fire is approximately 1.39 × 10^-7 cm. However, it is important to note that this experiment should only be attempted with extreme caution and proper safety measures in place, as focusing sunlight can be very dangerous and can cause fires or eye damage.
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A boy is trying to start a fire by focusing sunlighton a piece of paper using an equiconvex lens offocal length 10 cm. The diameter of the Sun is 1.39 ×109 m and its mean distance from the earthis 1.5 × 1011 m. What is the diameter of the Sun’simage on the paper? [2008]a)9.2 × 10–4 mb)6.5 × 10–4 mc)6.5 × 10–5 md)12.4 × 10–4 mCorrect answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A boy is trying to start a fire by focusing sunlighton a piece of paper using an equiconvex lens offocal length 10 cm. The diameter of the Sun is 1.39 ×109 m and its mean distance from the earthis 1.5 × 1011 m. What is the diameter of the Sun’simage on the paper? [2008]a)9.2 × 10–4 mb)6.5 × 10–4 mc)6.5 × 10–5 md)12.4 × 10–4 mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy is trying to start a fire by focusing sunlighton a piece of paper using an equiconvex lens offocal length 10 cm. The diameter of the Sun is 1.39 ×109 m and its mean distance from the earthis 1.5 × 1011 m. What is the diameter of the Sun’simage on the paper? [2008]a)9.2 × 10–4 mb)6.5 × 10–4 mc)6.5 × 10–5 md)12.4 × 10–4 mCorrect answer is option 'A'. Can you explain this answer?.
A boy is trying to start a fire by focusing sunlighton a piece of paper using an equiconvex lens offocal length 10 cm. The diameter of the Sun is 1.39 ×109 m and its mean distance from the earthis 1.5 × 1011 m. What is the diameter of the Sun’simage on the paper? [2008]a)9.2 × 10–4 mb)6.5 × 10–4 mc)6.5 × 10–5 md)12.4 × 10–4 mCorrect answer is option 'A'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A boy is trying to start a fire by focusing sunlighton a piece of paper using an equiconvex lens offocal length 10 cm. The diameter of the Sun is 1.39 ×109 m and its mean distance from the earthis 1.5 × 1011 m. What is the diameter of the Sun’simage on the paper? [2008]a)9.2 × 10–4 mb)6.5 × 10–4 mc)6.5 × 10–5 md)12.4 × 10–4 mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy is trying to start a fire by focusing sunlighton a piece of paper using an equiconvex lens offocal length 10 cm. The diameter of the Sun is 1.39 ×109 m and its mean distance from the earthis 1.5 × 1011 m. What is the diameter of the Sun’simage on the paper? [2008]a)9.2 × 10–4 mb)6.5 × 10–4 mc)6.5 × 10–5 md)12.4 × 10–4 mCorrect answer is option 'A'. Can you explain this answer?.
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