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If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height of the image?
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Given:
- Height of the object (h) = 10 cm
- Distance of the object from the mirror (u) = -36 cm (negative sign indicates that the object is placed in front of the mirror)
- Focal length of the mirror (f) = 12 cm
To find:
- Position of the image (v)
- Nature of the image (real/virtual, erect/inverted)
- Height of the image (h')
Solution:
Step 1: Calculating the position of the image (v)
Using the mirror formula:
1/f = 1/v - 1/u
Substituting the given values:
1/12 = 1/v - 1/-36
Simplifying the equation:
1/v = 1/12 + 1/36
1/v = 3/36 + 1/36
1/v = 4/36
v = 36/4
v = 9 cm
Therefore, the position of the image (v) is 9 cm.
Step 2: Determining the nature of the image
Since the object is placed in front of the mirror (u < 0),="" the="" image="" formed="" will="" be="" virtual="" and="" />
Step 3: Finding the height of the image (h')
Using the magnification formula:
magnification (m) = -v/u
Substituting the given values:
m = -9/-36
m = 1/4
Therefore, the magnification is 1/4.
The height of the image can be found using the formula:
h' = m * h
Substituting the calculated magnification and given object height:
h' = (1/4) * 10
h' = 2.5 cm
Therefore, the height of the image (h') is 2.5 cm.
Summary:
- The position of the image (v) is 9 cm.
- The nature of the image is virtual and erect.
- The height of the image (h') is 2.5 cm.
- Height of the object (h) = 10 cm
- Distance of the object from the mirror (u) = -36 cm (negative sign indicates that the object is placed in front of the mirror)
- Focal length of the mirror (f) = 12 cm
To find:
- Position of the image (v)
- Nature of the image (real/virtual, erect/inverted)
- Height of the image (h')
Solution:
Step 1: Calculating the position of the image (v)
Using the mirror formula:
1/f = 1/v - 1/u
Substituting the given values:
1/12 = 1/v - 1/-36
Simplifying the equation:
1/v = 1/12 + 1/36
1/v = 3/36 + 1/36
1/v = 4/36
v = 36/4
v = 9 cm
Therefore, the position of the image (v) is 9 cm.
Step 2: Determining the nature of the image
Since the object is placed in front of the mirror (u < 0),="" the="" image="" formed="" will="" be="" virtual="" and="" />
Step 3: Finding the height of the image (h')
Using the magnification formula:
magnification (m) = -v/u
Substituting the given values:
m = -9/-36
m = 1/4
Therefore, the magnification is 1/4.
The height of the image can be found using the formula:
h' = m * h
Substituting the calculated magnification and given object height:
h' = (1/4) * 10
h' = 2.5 cm
Therefore, the height of the image (h') is 2.5 cm.
Summary:
- The position of the image (v) is 9 cm.
- The nature of the image is virtual and erect.
- The height of the image (h') is 2.5 cm.
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If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height of the image?
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If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height 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 If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height of the image? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height of the image?.
If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height 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 If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height of the image? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an object of 10cm height is placed at a distance of 36cm form a converting mirror of focal length 12cm.Find the position,nature and height of the image?.
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