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The largest distance of the image of a real object from a convex mirror of focal length 20 cm can be
- a)20 cm
- b)Infinite
- c)10 cm
- d)Depends on the position of object
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The largest distance of the image of a real object from a convex mirro...
As x0 increases, v increases
⇒ vmax occurs when x0 = infinity
⇒ vmax = 20 cm
Most Upvoted Answer
The largest distance of the image of a real object from a convex mirro...
Explanation:
To understand why the largest distance of the image of a real object from a convex mirror of focal length 20 cm is 20 cm, let's first understand the behavior of convex mirrors.
Convex Mirrors:
- Convex mirrors are curved mirrors that bulge outwards and have a reflective surface on the outside.
- They have a positive focal length and are commonly used in rear-view mirrors of vehicles.
- Convex mirrors always produce virtual, erect, and diminished images of objects placed in front of them.
Focal Length and Image Formation:
- The focal length of a convex mirror is a measure of its curvature. A shorter focal length indicates a more curved mirror.
- When an object is placed in front of a convex mirror, light rays from the object diverge after reflection.
- The reflected rays appear to originate from a point behind the mirror, known as the virtual image.
- The position and size of the virtual image depend on the distance of the object from the mirror and the focal length of the mirror.
Maximum Distance for Image Formation:
- The maximum distance at which a convex mirror can form an image is when the object is placed at the focal point of the mirror.
- In this case, the reflected rays will appear to be parallel, and the virtual image will be formed at infinity.
- The distance of the object from the mirror is equal to the focal length of the mirror, which is 20 cm in this case.
- Therefore, the largest distance of the image of a real object from a convex mirror of focal length 20 cm is 20 cm.
Options Analysis:
- Option (a) is correct because it states that the largest distance can be 20 cm, which is the case when the object is placed at the focal point.
- Option (b) is incorrect because convex mirrors cannot form real images, so the image distance cannot be infinite.
- Option (c) is incorrect because the maximum image distance is limited by the focal length of the mirror.
- Option (d) is incorrect because the distance of the image does not depend on the position of the object, but rather on the focal length of the mirror.
Therefore, the correct answer is option (a) - 20 cm.
To understand why the largest distance of the image of a real object from a convex mirror of focal length 20 cm is 20 cm, let's first understand the behavior of convex mirrors.
Convex Mirrors:
- Convex mirrors are curved mirrors that bulge outwards and have a reflective surface on the outside.
- They have a positive focal length and are commonly used in rear-view mirrors of vehicles.
- Convex mirrors always produce virtual, erect, and diminished images of objects placed in front of them.
Focal Length and Image Formation:
- The focal length of a convex mirror is a measure of its curvature. A shorter focal length indicates a more curved mirror.
- When an object is placed in front of a convex mirror, light rays from the object diverge after reflection.
- The reflected rays appear to originate from a point behind the mirror, known as the virtual image.
- The position and size of the virtual image depend on the distance of the object from the mirror and the focal length of the mirror.
Maximum Distance for Image Formation:
- The maximum distance at which a convex mirror can form an image is when the object is placed at the focal point of the mirror.
- In this case, the reflected rays will appear to be parallel, and the virtual image will be formed at infinity.
- The distance of the object from the mirror is equal to the focal length of the mirror, which is 20 cm in this case.
- Therefore, the largest distance of the image of a real object from a convex mirror of focal length 20 cm is 20 cm.
Options Analysis:
- Option (a) is correct because it states that the largest distance can be 20 cm, which is the case when the object is placed at the focal point.
- Option (b) is incorrect because convex mirrors cannot form real images, so the image distance cannot be infinite.
- Option (c) is incorrect because the maximum image distance is limited by the focal length of the mirror.
- Option (d) is incorrect because the distance of the image does not depend on the position of the object, but rather on the focal length of the mirror.
Therefore, the correct answer is option (a) - 20 cm.
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The largest distance of the image of a real object from a convex mirror of focal length 20 cm can be a)20 cm b)Infinite c)10 cmd)Depends on the position of objectCorrect answer is option 'A'. Can you explain this answer?
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