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A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively
- a)f and I/4
- b)3f/4 and I/2
- c)f and 3I/4
- d)f/2 and I/2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A lens having focal length f and aperture of diameter d forms an image...
Focal length of the lens remains same.
Intensity of image formed by lens is proportional to area exposed to incident light from object.
i.e. Intensity ∝ area
Intensity of image formed by lens is proportional to area exposed to incident light from object.
i.e. Intensity ∝ area
After blocking, exposed area,
Hence, focal length of a lens = f, intensity of the image = 3I/4
Most Upvoted Answer
A lens having focal length f and aperture of diameter d forms an image...
Given:
- Lens with focal length f and aperture diameter d forms an image of intensity I.
- Aperture of diameter d/2 in the central region of the lens is covered by a black paper.
To find:
- The new focal length of the lens.
- The new intensity of the image.
Solution:
When the aperture is covered by black paper, it acts as a stop, limiting the amount of light passing through the lens. This causes a decrease in the intensity of the image formed.
1. Effect of covering the aperture:
- When the aperture is covered, the effective diameter of the lens is reduced to d/2.
- The area of the effective aperture is proportional to the square of its diameter. So, the area of the effective aperture is reduced to (d/2)^2 = d^2/4.
- Therefore, the amount of light passing through the lens is reduced by a factor of 1/4.
2. Effect on focal length:
- The focal length of a lens is determined by its shape and refractive index, and it does not depend on the diameter of the aperture.
- Therefore, covering the aperture does not change the focal length of the lens. Hence, the new focal length of the lens remains f.
3. Effect on intensity:
- The intensity of the image is given by the formula I ∝ (1/f^2).
- Since the focal length remains unchanged, the intensity of the image is directly proportional to 1/f^2. Therefore, the intensity of the image remains I.
Hence, the new focal length of the lens is f, and the new intensity of the image is 3I/4. Therefore, the correct option is (c) f and 3I/4.
- Lens with focal length f and aperture diameter d forms an image of intensity I.
- Aperture of diameter d/2 in the central region of the lens is covered by a black paper.
To find:
- The new focal length of the lens.
- The new intensity of the image.
Solution:
When the aperture is covered by black paper, it acts as a stop, limiting the amount of light passing through the lens. This causes a decrease in the intensity of the image formed.
1. Effect of covering the aperture:
- When the aperture is covered, the effective diameter of the lens is reduced to d/2.
- The area of the effective aperture is proportional to the square of its diameter. So, the area of the effective aperture is reduced to (d/2)^2 = d^2/4.
- Therefore, the amount of light passing through the lens is reduced by a factor of 1/4.
2. Effect on focal length:
- The focal length of a lens is determined by its shape and refractive index, and it does not depend on the diameter of the aperture.
- Therefore, covering the aperture does not change the focal length of the lens. Hence, the new focal length of the lens remains f.
3. Effect on intensity:
- The intensity of the image is given by the formula I ∝ (1/f^2).
- Since the focal length remains unchanged, the intensity of the image is directly proportional to 1/f^2. Therefore, the intensity of the image remains I.
Hence, the new focal length of the lens is f, and the new intensity of the image is 3I/4. Therefore, the correct option is (c) f and 3I/4.
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A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer?
Question Description
A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer?.
A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer?.
Solutions for A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectivelya)f and I/4b)3f/4 and I/2c)f and 3I/4d)f/2 and I/2Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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