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A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image is
- a)0.25 m
- b)0.33 m
- c)0.5 m
- d)0.67 m
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A boy of height 1 m stands in front of a convex mirror. His distance f...
Understanding the Convex Mirror Setup
In this scenario, we have a boy of height 1 m standing in front of a convex mirror. The distance of the boy from the mirror is equal to the focal length (f) of the mirror.
Key Concepts of Convex Mirrors
- Convex Mirror Characteristics:
- Always produces virtual, erect, and diminished images.
- The focal length (f) is positive for convex mirrors.
- Mirror Formula:
- The mirror formula is given by 1/f = 1/v + 1/u, where:
- f = focal length
- v = image distance (from the mirror)
- u = object distance (from the mirror)
Given Values
- Height of the boy (h) = 1 m
- Object distance (u) = -f (since u is measured against the direction of incident light)
Calculating Image Height
1. Using the Mirror Formula:
- Since the distance from the mirror is equal to its focal length, let f = u.
- Substitute u = -f into the mirror formula:
- 1/f = 1/v - 1/f
- Rearranging gives: 1/v = 2/f, so v = f/2.
2. Magnification (m):
- Magnification is given by m = h'/h = -v/u.
- Substituting the values:
- m = - (f/2) / (-f) = 1/2.
3. Finding Image Height (h'):
- h' = m * h = (1/2) * 1 m = 0.5 m.
Conclusion
Therefore, the height of the image of the boy is 0.5 m, confirming that option 'C' is correct.
In this scenario, we have a boy of height 1 m standing in front of a convex mirror. The distance of the boy from the mirror is equal to the focal length (f) of the mirror.
Key Concepts of Convex Mirrors
- Convex Mirror Characteristics:
- Always produces virtual, erect, and diminished images.
- The focal length (f) is positive for convex mirrors.
- Mirror Formula:
- The mirror formula is given by 1/f = 1/v + 1/u, where:
- f = focal length
- v = image distance (from the mirror)
- u = object distance (from the mirror)
Given Values
- Height of the boy (h) = 1 m
- Object distance (u) = -f (since u is measured against the direction of incident light)
Calculating Image Height
1. Using the Mirror Formula:
- Since the distance from the mirror is equal to its focal length, let f = u.
- Substitute u = -f into the mirror formula:
- 1/f = 1/v - 1/f
- Rearranging gives: 1/v = 2/f, so v = f/2.
2. Magnification (m):
- Magnification is given by m = h'/h = -v/u.
- Substituting the values:
- m = - (f/2) / (-f) = 1/2.
3. Finding Image Height (h'):
- h' = m * h = (1/2) * 1 m = 0.5 m.
Conclusion
Therefore, the height of the image of the boy is 0.5 m, confirming that option 'C' is correct.
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Community Answer
A boy of height 1 m stands in front of a convex mirror. His distance f...
Let f be focal length of the convex mirror.
According to new cartesian sign convention
Object distance, u = −f, focal length = +f
Using mirror formula,
The image is formed at a distance f/2 behind the mirror. It is a virtual image.
According to new cartesian sign convention
Object distance, u = −f, focal length = +f
Using mirror formula,
The image is formed at a distance f/2 behind the mirror. It is a virtual image.
∴ h1 = mh0
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A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isa)0.25 mb)0.33 mc)0.5 md)0.67 mCorrect answer is option 'C'. Can you explain this answer?
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A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isa)0.25 mb)0.33 mc)0.5 md)0.67 mCorrect answer is option 'C'. 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 A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isa)0.25 mb)0.33 mc)0.5 md)0.67 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isa)0.25 mb)0.33 mc)0.5 md)0.67 mCorrect answer is option 'C'. Can you explain this answer?.
A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isa)0.25 mb)0.33 mc)0.5 md)0.67 mCorrect answer is option 'C'. 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 A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isa)0.25 mb)0.33 mc)0.5 md)0.67 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image isa)0.25 mb)0.33 mc)0.5 md)0.67 mCorrect answer is option 'C'. Can you explain this answer?.
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