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A convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.?
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A convex mirror used for rear view on an automobile has a radius of cu...
Given:
- Radius of curvature of convex mirror, R = 6m
- Object distance, u = -10m (negative sign indicates object is placed in front of the mirror)
To find:
- Position, nature and size of the image formed by the mirror.
Solution:
Step 1: Using mirror formula, we can find the image distance (v).
1/f = 1/u + 1/v where f = R/2 (for a spherical mirror)
1/(R/2) = 1/u + 1/v
v = (R/2) * (1 - u/R)
v = (6/2) * (1 + 10/6) = 7m
The image is formed at a distance of 7m from the mirror.
Step 2: Using magnification formula, we can find the magnification (m) of the image formed.
m = -v/u
m = -7/-10 = 0.7
The negative sign indicates that the image is formed behind the mirror and it is virtual (not real). The magnification tells us that the image is smaller than the object.
Step 3: Using the mirror formula again, we can find the size of the image formed.
1/v - 1/u = 1/f
1/v = 1/f + 1/u
1/v = 1/3 + 1/-10
v = -15/7m
The size of the image can be found using the magnification formula.
m = hi/ho = -v/u
hi = m * ho
hi = 0.7 * 1m (Assuming the height of the object is 1m)
hi = 0.7m
The image formed is virtual, erect and smaller than the object. It is formed at a distance of 7m behind the mirror and its height is 0.7m.
- Radius of curvature of convex mirror, R = 6m
- Object distance, u = -10m (negative sign indicates object is placed in front of the mirror)
To find:
- Position, nature and size of the image formed by the mirror.
Solution:
Step 1: Using mirror formula, we can find the image distance (v).
1/f = 1/u + 1/v where f = R/2 (for a spherical mirror)
1/(R/2) = 1/u + 1/v
v = (R/2) * (1 - u/R)
v = (6/2) * (1 + 10/6) = 7m
The image is formed at a distance of 7m from the mirror.
Step 2: Using magnification formula, we can find the magnification (m) of the image formed.
m = -v/u
m = -7/-10 = 0.7
The negative sign indicates that the image is formed behind the mirror and it is virtual (not real). The magnification tells us that the image is smaller than the object.
Step 3: Using the mirror formula again, we can find the size of the image formed.
1/v - 1/u = 1/f
1/v = 1/f + 1/u
1/v = 1/3 + 1/-10
v = -15/7m
The size of the image can be found using the magnification formula.
m = hi/ho = -v/u
hi = m * ho
hi = 0.7 * 1m (Assuming the height of the object is 1m)
hi = 0.7m
The image formed is virtual, erect and smaller than the object. It is formed at a distance of 7m behind the mirror and its height is 0.7m.
Community Answer
A convex mirror used for rear view on an automobile has a radius of cu...
The image will be between focus and pole and it will be erect and diminished
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A convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.?
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A convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.? 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 convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.?.
A convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.? 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 convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex mirror used for rear view on an automobile has a radius of curvature of 6 m. If a car is located at 10 m from this mirror, find the position, nature and size of the image.?.
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