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The focal length of a concave mirror is 20cm.Find the position of the image of an object placed at a distance of 30cm from the lens and also find it's linear magnification.?
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The focal length of a concave mirror is 20cm.Find the position of the ...
Understanding the Problem
To find the position of the image formed by a concave mirror and its linear magnification, we can use the mirror formula and magnification formula.
Given Information
- Focal Length (f) = -20 cm (negative for concave mirror)
- Object Distance (u) = -30 cm (negative as per sign convention)
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
Calculating Image Distance (v)
Using the values:
1. Substitute into the formula:
1/(-20) = 1/v + 1/(-30)
2. Rearranging gives:
1/v = 1/(-20) + 1/(-30)
3. Finding a common denominator and solving yields:
1/v = -3/60 - 2/60 = -5/60
Therefore, v = -12 cm.
Interpreting the Result
The negative value of v indicates that the image is formed on the same side as the object, which is typical for concave mirrors.
Calculating Linear Magnification (m)
The magnification formula is given by:
m = -v/u
1. Substitute the values:
m = -(-12)/(-30)
m = 12/30 = 0.4
Conclusion
- The position of the image is at 12 cm in front of the mirror (real image).
- The linear magnification of the image is 0.4, indicating the image is smaller than the object.
To find the position of the image formed by a concave mirror and its linear magnification, we can use the mirror formula and magnification formula.
Given Information
- Focal Length (f) = -20 cm (negative for concave mirror)
- Object Distance (u) = -30 cm (negative as per sign convention)
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
Calculating Image Distance (v)
Using the values:
1. Substitute into the formula:
1/(-20) = 1/v + 1/(-30)
2. Rearranging gives:
1/v = 1/(-20) + 1/(-30)
3. Finding a common denominator and solving yields:
1/v = -3/60 - 2/60 = -5/60
Therefore, v = -12 cm.
Interpreting the Result
The negative value of v indicates that the image is formed on the same side as the object, which is typical for concave mirrors.
Calculating Linear Magnification (m)
The magnification formula is given by:
m = -v/u
1. Substitute the values:
m = -(-12)/(-30)
m = 12/30 = 0.4
Conclusion
- The position of the image is at 12 cm in front of the mirror (real image).
- The linear magnification of the image is 0.4, indicating the image is smaller than the object.
Community Answer
The focal length of a concave mirror is 20cm.Find the position of the ...
Sorry it's a mistake it is mirror not lens .
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The focal length of a concave mirror is 20cm.Find the position of the image of an object placed at a distance of 30cm from the lens and also find it's linear magnification.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The focal length of a concave mirror is 20cm.Find the position of the image of an object placed at a distance of 30cm from the lens and also find it's linear magnification.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The focal length of a concave mirror is 20cm.Find the position of the image of an object placed at a distance of 30cm from the lens and also find it's linear magnification.?.
The focal length of a concave mirror is 20cm.Find the position of the image of an object placed at a distance of 30cm from the lens and also find it's linear magnification.? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The focal length of a concave mirror is 20cm.Find the position of the image of an object placed at a distance of 30cm from the lens and also find it's linear magnification.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The focal length of a concave mirror is 20cm.Find the position of the image of an object placed at a distance of 30cm from the lens and also find it's linear magnification.?.
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