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A linear object is placed at a distance equal to focal length of a convex mirror. Its image is formed
- a)at infinite distance
- b)at the principal focus of mirror
- c)behind the mirror at a distance f/2
- d)in front of mirror at a distance f/2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A linear object is placed at a distance equal to focal length of a con...
When a linear object is placed at a distance equal to focal length of a convex mirror then its virtual image is form ed behind the mirror at a distance f/2
As per sign convention u = - f and focal length o f convex mirror is + ve, hence from mirror formula
we have
or 
or 
As per sign convention u = - f and focal length o f convex mirror is + ve, hence from mirror formula
we have or or Most Upvoted Answer
A linear object is placed at a distance equal to focal length of a con...
When an object is placed at a distance equal to the focal length of a convex mirror, its image is formed behind the mirror at a distance f/2. This can be explained using the laws of reflection and the properties of convex mirrors.
Law of Reflection:
According to the law of reflection, the incident ray, the reflected ray, and the normal to the mirror surface at the point of incidence, all lie in the same plane. The angle of incidence is equal to the angle of reflection.
Properties of Convex Mirrors:
1. Convex mirrors are curved outward, meaning that the reflecting surface bulges outward.
2. The focal length of a convex mirror is always positive.
3. The image formed by a convex mirror is always virtual, diminished, and upright.
Explanation:
1. When an object is placed at a distance equal to the focal length of a convex mirror, the incident rays from the object are parallel to each other.
2. As these parallel rays strike the convex mirror, they reflect off in different directions, diverging away from each other.
3. By extending the reflected rays backward, they appear to meet at a point behind the mirror.
4. This point where the reflected rays appear to meet is the virtual image of the object.
5. The virtual image formed is always upright, diminished in size, and located behind the mirror.
6. The distance between the mirror and the virtual image is half the focal length of the convex mirror (f/2).
7. Therefore, the correct answer is option 'C' - the image is formed behind the mirror at a distance f/2.
Significance of the Image Distance:
The fact that the virtual image is formed at a distance f/2 is significant because it helps determine the size and position of the image. The distance of f/2 indicates that the image is located closer to the mirror compared to the focal point (f) itself. This means that the virtual image formed is magnified compared to the actual object.
Law of Reflection:
According to the law of reflection, the incident ray, the reflected ray, and the normal to the mirror surface at the point of incidence, all lie in the same plane. The angle of incidence is equal to the angle of reflection.
Properties of Convex Mirrors:
1. Convex mirrors are curved outward, meaning that the reflecting surface bulges outward.
2. The focal length of a convex mirror is always positive.
3. The image formed by a convex mirror is always virtual, diminished, and upright.
Explanation:
1. When an object is placed at a distance equal to the focal length of a convex mirror, the incident rays from the object are parallel to each other.
2. As these parallel rays strike the convex mirror, they reflect off in different directions, diverging away from each other.
3. By extending the reflected rays backward, they appear to meet at a point behind the mirror.
4. This point where the reflected rays appear to meet is the virtual image of the object.
5. The virtual image formed is always upright, diminished in size, and located behind the mirror.
6. The distance between the mirror and the virtual image is half the focal length of the convex mirror (f/2).
7. Therefore, the correct answer is option 'C' - the image is formed behind the mirror at a distance f/2.
Significance of the Image Distance:
The fact that the virtual image is formed at a distance f/2 is significant because it helps determine the size and position of the image. The distance of f/2 indicates that the image is located closer to the mirror compared to the focal point (f) itself. This means that the virtual image formed is magnified compared to the actual object.
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Community Answer
A linear object is placed at a distance equal to focal length of a con...
To understand why the correct answer is option 'C', let's analyze the concept of a convex mirror and its image formation.
Convex Mirror:
A convex mirror is a curved mirror with a reflecting surface that bulges outwards. It is also known as a diverging mirror because it diverges light rays that strike its surface.
Focal Length:
The focal length (f) of a convex mirror is always positive. It is the distance between the mirror and its principal focus (F). In convex mirrors, the focal length is half the radius of curvature (R).
Now, let's consider the scenario described in the question:
Alinear object is placed at a distance equal to the focal length of a convex mirror.
When an object is placed at a distance equal to the focal length of a convex mirror, the object is said to be at the focus (F) of the mirror. Let's analyze what happens in this situation:
1. Ray Diagram:
To understand the image formation, we can draw a ray diagram. Consider a ray of light parallel to the principal axis that strikes the convex mirror.
2. Ray Reflection:
According to the laws of reflection, the ray of light will reflect off the convex mirror. Since convex mirrors always diverge light rays, the reflected ray will appear to come from the principal focus (F) of the mirror.
3. Virtual Image Formation:
Since the reflected ray appears to come from the principal focus, the image formed by the convex mirror will be a virtual image. Virtual images are formed when the reflected rays do not actually converge at a point but only appear to diverge from a specific location.
4. Behind the Mirror:
In the given scenario, the virtual image will be formed behind the convex mirror. The distance of the virtual image from the mirror will be equal to half the focal length (f/2). This is because the focal length is the distance between the mirror and its principal focus, and the image is formed at the principal focus.
Therefore, the correct answer is option 'C' - the image is formed behind the mirror at a distance f/2.
Convex Mirror:
A convex mirror is a curved mirror with a reflecting surface that bulges outwards. It is also known as a diverging mirror because it diverges light rays that strike its surface.
Focal Length:
The focal length (f) of a convex mirror is always positive. It is the distance between the mirror and its principal focus (F). In convex mirrors, the focal length is half the radius of curvature (R).
Now, let's consider the scenario described in the question:
Alinear object is placed at a distance equal to the focal length of a convex mirror.
When an object is placed at a distance equal to the focal length of a convex mirror, the object is said to be at the focus (F) of the mirror. Let's analyze what happens in this situation:
1. Ray Diagram:
To understand the image formation, we can draw a ray diagram. Consider a ray of light parallel to the principal axis that strikes the convex mirror.
2. Ray Reflection:
According to the laws of reflection, the ray of light will reflect off the convex mirror. Since convex mirrors always diverge light rays, the reflected ray will appear to come from the principal focus (F) of the mirror.
3. Virtual Image Formation:
Since the reflected ray appears to come from the principal focus, the image formed by the convex mirror will be a virtual image. Virtual images are formed when the reflected rays do not actually converge at a point but only appear to diverge from a specific location.
4. Behind the Mirror:
In the given scenario, the virtual image will be formed behind the convex mirror. The distance of the virtual image from the mirror will be equal to half the focal length (f/2). This is because the focal length is the distance between the mirror and its principal focus, and the image is formed at the principal focus.
Therefore, the correct answer is option 'C' - the image is formed behind the mirror at a distance f/2.
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A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer?
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A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer?.
A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer?.
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A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A linear object is placed at a distance equal to focal length of a convex mirror.Its image is formeda)at infinite distanceb)at the principal focus of mirrorc)behind the mirror at a distance f/2d)in front of mirror at a distance f/2Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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