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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 the object
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The largest distance of the image of a real object from a convex mirro...
We are given that:
Focal length = 20 cm
In a convex mirror image is formed between focal length and mirror.
So the maximum distance is f i.e. focal length of the mirror.
Now
f = 20 / 2 = 10 cm
Thus the largest distance of an image from a convex mirror is 10 cm.
Focal length = 20 cm
In a convex mirror image is formed between focal length and mirror.
So the maximum distance is f i.e. focal length of the mirror.
Now
f = 20 / 2 = 10 cm
Thus the largest distance of an image from a convex mirror is 10 cm.
Most Upvoted Answer
The largest distance of the image of a real object from a convex mirro...
The correct answer to this question is option 'C' - 10 cm. Let's understand why.
Convex mirrors are curved mirrors that bulge outwards. They have a reflective surface on the outer side, and the center of curvature lies behind the mirror. The focal length of a convex mirror is considered negative.
Given that the focal length of the convex mirror is 20 cm, we know that it is negative and can be written as -20 cm.
To find the largest distance of the image of a real object, we need to consider two cases:
Case 1: When the object is placed at infinity
When the object is placed at infinity, the rays of light coming from the object are parallel to each other. These parallel rays are reflected by the convex mirror in such a way that they appear to diverge from a single point behind the mirror, known as the virtual focus.
In this case, the image formed by the convex mirror is a virtual image. The distance of this virtual image from the mirror is equal to the focal length, which is 20 cm. However, since the question asks for the largest distance, we need to consider a different scenario.
Case 2: When the object is placed at a finite distance
When the object is placed at a finite distance from the convex mirror, the rays of light coming from the object diverge. These diverging rays are reflected by the convex mirror in such a way that they appear to come from a single point behind the mirror, known as the real focus.
The distance between the object and the convex mirror is denoted as 'u', and the distance between the image and the convex mirror is denoted as 'v'.
The mirror formula gives us the relationship between these distances:
1/f = 1/v - 1/u
Since the object is real, the distance 'u' is always positive. As the object moves closer to the mirror, 'u' decreases. To find the largest distance of the image, we need to consider the case where 'u' is minimum.
In the given scenario, the largest distance of the image can be achieved when 'u' is minimum, which is equal to the focal length of the mirror. Therefore, the largest distance of the image is 10 cm (which is half the focal length).
Hence, the correct answer is option 'C' - 10 cm.
Convex mirrors are curved mirrors that bulge outwards. They have a reflective surface on the outer side, and the center of curvature lies behind the mirror. The focal length of a convex mirror is considered negative.
Given that the focal length of the convex mirror is 20 cm, we know that it is negative and can be written as -20 cm.
To find the largest distance of the image of a real object, we need to consider two cases:
Case 1: When the object is placed at infinity
When the object is placed at infinity, the rays of light coming from the object are parallel to each other. These parallel rays are reflected by the convex mirror in such a way that they appear to diverge from a single point behind the mirror, known as the virtual focus.
In this case, the image formed by the convex mirror is a virtual image. The distance of this virtual image from the mirror is equal to the focal length, which is 20 cm. However, since the question asks for the largest distance, we need to consider a different scenario.
Case 2: When the object is placed at a finite distance
When the object is placed at a finite distance from the convex mirror, the rays of light coming from the object diverge. These diverging rays are reflected by the convex mirror in such a way that they appear to come from a single point behind the mirror, known as the real focus.
The distance between the object and the convex mirror is denoted as 'u', and the distance between the image and the convex mirror is denoted as 'v'.
The mirror formula gives us the relationship between these distances:
1/f = 1/v - 1/u
Since the object is real, the distance 'u' is always positive. As the object moves closer to the mirror, 'u' decreases. To find the largest distance of the image, we need to consider the case where 'u' is minimum.
In the given scenario, the largest distance of the image can be achieved when 'u' is minimum, which is equal to the focal length of the mirror. Therefore, the largest distance of the image is 10 cm (which is half the focal length).
Hence, the correct answer is option 'C' - 10 cm.
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