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The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.
- a)1.25 cm
- b)2.5 cm
- c)1.05 cm
- d)2 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The size of the image of an object, which is at infinity, as formed b...
Given:
- Object distance, u = infinity
- Focal length of convex lens, f1 = 30 cm
- Size of image formed by convex lens, v1 = 2 cm
- Focal length of concave lens, f2 = -20 cm (negative sign indicates concave lens)
- Distance between convex lens and concave lens, d = 26 cm
To find:
- Size of image formed by the combination of lenses, v2
We can use the lens formula:
1/f = 1/u + 1/v
For the convex lens, when the object is at infinity:
1/f1 = 1/u + 1/v1
1/30 = 0 + 1/v1
v1 = 30 cm
Now, let's consider the combination of lenses. We can use the formula:
1/f = 1/f1 + 1/f2 - d/f1f2
where d is the distance between the two lenses.
Substituting the values:
1/f = 1/30 - 1/20 - 26/(30 x -20)
1/f = -1/60 - 13/600
1/f = -14/600
f = -42.86 cm
Note that the negative sign indicates that the combination of lenses acts like a concave lens.
Using the lens formula again, we can find the size of the image formed by the combination of lenses:
1/f = 1/u + 1/v2
1/-42.86 = 0 + 1/v2
v2 = -42.86 cm
Note that the negative sign indicates that the image is virtual. To find the size of the image, we can use the magnification formula:
m = -v2/v1
m = -(-42.86)/30
m = 1.43
The magnification is positive, which means that the image is upright. The size of the image is given by:
v2 = m x v1
v2 = 1.43 x 2 cm
v2 = 2.86 cm
Therefore, the new size of the image formed by the combination of lenses is 2.86 cm, which is closest to option (B) 2.5 cm.
- Object distance, u = infinity
- Focal length of convex lens, f1 = 30 cm
- Size of image formed by convex lens, v1 = 2 cm
- Focal length of concave lens, f2 = -20 cm (negative sign indicates concave lens)
- Distance between convex lens and concave lens, d = 26 cm
To find:
- Size of image formed by the combination of lenses, v2
We can use the lens formula:
1/f = 1/u + 1/v
For the convex lens, when the object is at infinity:
1/f1 = 1/u + 1/v1
1/30 = 0 + 1/v1
v1 = 30 cm
Now, let's consider the combination of lenses. We can use the formula:
1/f = 1/f1 + 1/f2 - d/f1f2
where d is the distance between the two lenses.
Substituting the values:
1/f = 1/30 - 1/20 - 26/(30 x -20)
1/f = -1/60 - 13/600
1/f = -14/600
f = -42.86 cm
Note that the negative sign indicates that the combination of lenses acts like a concave lens.
Using the lens formula again, we can find the size of the image formed by the combination of lenses:
1/f = 1/u + 1/v2
1/-42.86 = 0 + 1/v2
v2 = -42.86 cm
Note that the negative sign indicates that the image is virtual. To find the size of the image, we can use the magnification formula:
m = -v2/v1
m = -(-42.86)/30
m = 1.43
The magnification is positive, which means that the image is upright. The size of the image is given by:
v2 = m x v1
v2 = 1.43 x 2 cm
v2 = 2.86 cm
Therefore, the new size of the image formed by the combination of lenses is 2.86 cm, which is closest to option (B) 2.5 cm.
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Community Answer
The size of the image of an object, which is at infinity, as formed b...
Given:
- Object is at infinity
- Convex lens has focal length f1 = 30 cm
- Image formed by convex lens has size h1 = 2 cm
- Concave lens has focal length f2 = -20 cm
- Concave lens is placed at a distance of d = 26 cm from the convex lens
To find:
- Size of the new image formed after passing through the concave lens
Approach:
- Use the thin lens formula and magnification formula to find the image size formed by the convex lens
- Use the formula for the effective focal length of two lenses in contact to find the effective focal length of the system
- Use the thin lens formula and magnification formula again to find the size of the final image formed by the concave lens
Solution:
1. Image formed by convex lens:
Using the thin lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance, we can find the image distance di for an object at infinity (do = infinity):
1/f1 = 1/infinity + 1/di
di = f1
Using the magnification formula m = -di/do = hi/ho, where m is the magnification, hi is the image height, and ho is the object height, we can find the image height hi:
m = -di/do = -f1/infinity = 1
hi/ho = m
hi = ho = h1 = 2 cm
Therefore, the image formed by the convex lens has the same size as the object, which is 2 cm.
2. Effective focal length of the system:
When two lenses are in contact, the effective focal length feff of the system is given by:
1/feff = 1/f1 + 1/f2 - d/(f1*f2)
Substituting the given values, we get:
1/feff = 1/30 - 1/20 - 26/(30*20)
feff = -60 cm
Note that the negative sign indicates that the system behaves as a diverging lens.
3. Image formed by the concave lens:
Using the thin lens formula and magnification formula again, we can find the image height hi2 formed by the concave lens:
1/feff = 1/do + 1/di2
di2 = 1/(1/feff - 1/do)
di2 = -26 cm (since the image is virtual)
m = -di2/do = hi2/ho
hi2 = m*ho = -di2*h1/30
hi2 = -(-26)*2/30 = 1.73 cm
Therefore, the size of the final image formed by the concave lens is 1.73 cm (rounded to 2 decimal places).
Answer:
Option (b) 2.5 cm
- Object is at infinity
- Convex lens has focal length f1 = 30 cm
- Image formed by convex lens has size h1 = 2 cm
- Concave lens has focal length f2 = -20 cm
- Concave lens is placed at a distance of d = 26 cm from the convex lens
To find:
- Size of the new image formed after passing through the concave lens
Approach:
- Use the thin lens formula and magnification formula to find the image size formed by the convex lens
- Use the formula for the effective focal length of two lenses in contact to find the effective focal length of the system
- Use the thin lens formula and magnification formula again to find the size of the final image formed by the concave lens
Solution:
1. Image formed by convex lens:
Using the thin lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance, we can find the image distance di for an object at infinity (do = infinity):
1/f1 = 1/infinity + 1/di
di = f1
Using the magnification formula m = -di/do = hi/ho, where m is the magnification, hi is the image height, and ho is the object height, we can find the image height hi:
m = -di/do = -f1/infinity = 1
hi/ho = m
hi = ho = h1 = 2 cm
Therefore, the image formed by the convex lens has the same size as the object, which is 2 cm.
2. Effective focal length of the system:
When two lenses are in contact, the effective focal length feff of the system is given by:
1/feff = 1/f1 + 1/f2 - d/(f1*f2)
Substituting the given values, we get:
1/feff = 1/30 - 1/20 - 26/(30*20)
feff = -60 cm
Note that the negative sign indicates that the system behaves as a diverging lens.
3. Image formed by the concave lens:
Using the thin lens formula and magnification formula again, we can find the image height hi2 formed by the concave lens:
1/feff = 1/do + 1/di2
di2 = 1/(1/feff - 1/do)
di2 = -26 cm (since the image is virtual)
m = -di2/do = hi2/ho
hi2 = m*ho = -di2*h1/30
hi2 = -(-26)*2/30 = 1.73 cm
Therefore, the size of the final image formed by the concave lens is 1.73 cm (rounded to 2 decimal places).
Answer:
Option (b) 2.5 cm
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Question Description
The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer?.
The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and image at a distance of 26 cm from the convex lens, calculate the new size of the image.a)1.25 cmb)2.5 cmc)1.05 cmd)2 cmCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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