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An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position?
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An object is placed at a distance of 15 cm from a convex mirror of foc...
Understanding the Setup
To analyze the image formed by a convex mirror, we can use the mirror formula and the characteristics of convex mirrors.
Given Data
- Object distance (u) = -15 cm (negative as per sign convention)
- Focal length (f) = +6 cm (positive for convex mirrors)
Using the Mirror Formula
The mirror formula is given by:
1/f = 1/v + 1/u
Where:
- f = focal length
- v = image distance
- u = object distance
Substituting the known values:
1/6 = 1/v + 1/(-15)
Calculating Image Distance (v)
Rearranging the formula gives:
1/v = 1/6 + 1/15
Finding a common denominator (30):
1/v = (5 + 2)/30
1/v = 7/30
Thus, v = 30/7 = approximately 4.29 cm
Nature of the Image
- The image distance (v) is positive, indicating that the image is formed on the same side as the object.
- Since this is a convex mirror, the image will also be virtual and upright.
Conclusion
- Image Position: Approximately 4.29 cm behind the mirror.
- Nature: Virtual, upright, and diminished (smaller than the object).
Convex mirrors are widely used in vehicles for rear-view mirrors due to their ability to provide a wider field of view while ensuring the safety of the driver.
To analyze the image formed by a convex mirror, we can use the mirror formula and the characteristics of convex mirrors.
Given Data
- Object distance (u) = -15 cm (negative as per sign convention)
- Focal length (f) = +6 cm (positive for convex mirrors)
Using the Mirror Formula
The mirror formula is given by:
1/f = 1/v + 1/u
Where:
- f = focal length
- v = image distance
- u = object distance
Substituting the known values:
1/6 = 1/v + 1/(-15)
Calculating Image Distance (v)
Rearranging the formula gives:
1/v = 1/6 + 1/15
Finding a common denominator (30):
1/v = (5 + 2)/30
1/v = 7/30
Thus, v = 30/7 = approximately 4.29 cm
Nature of the Image
- The image distance (v) is positive, indicating that the image is formed on the same side as the object.
- Since this is a convex mirror, the image will also be virtual and upright.
Conclusion
- Image Position: Approximately 4.29 cm behind the mirror.
- Nature: Virtual, upright, and diminished (smaller than the object).
Convex mirrors are widely used in vehicles for rear-view mirrors due to their ability to provide a wider field of view while ensuring the safety of the driver.
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An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position?
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An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position? 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 An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position?.
An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position? 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 An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is placed at a distance of 15 cm from a convex mirror of focal length 6 cm. find nature and position?.
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