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A concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror?
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Calculation of Radius of Curvature of a Concave Mirror
To calculate the radius of curvature of a concave mirror, one needs to use the mirror formula:
1/f = 1/v + 1/u
Where,
f = focal length of the mirror
v = image distance
u = object distance
Given Data:
Object distance, u = -10 cm (negative sign indicates object is placed in front of the mirror)
Magnification, m = 3
Solution:
1. Magnification is defined as the ratio of the image height to the object height.
m = hi/ho
where hi and ho are the image and object heights respectively.
2. For a concave mirror, magnification is always negative (since it is an inverted image).
m = -3
3. Image distance can be calculated using the magnification formula:
m = -v/u
=> -3 = -v/(-10)
=> v = -30 cm
4. Now, we can use the mirror formula to find the focal length of the mirror.
1/f = 1/v + 1/u
=> 1/f = 1/-30 + 1/(-10)
=> 1/f = -1/15
=> f = -15 cm
5. The radius of curvature (R) of the mirror is twice the focal length (f).
R = 2f
=> R = -30 cm
Conclusion:
The radius of curvature of the concave mirror is -30 cm. This means that the mirror has a focal length of -15 cm (since f = R/2).
To calculate the radius of curvature of a concave mirror, one needs to use the mirror formula:
1/f = 1/v + 1/u
Where,
f = focal length of the mirror
v = image distance
u = object distance
Given Data:
Object distance, u = -10 cm (negative sign indicates object is placed in front of the mirror)
Magnification, m = 3
Solution:
1. Magnification is defined as the ratio of the image height to the object height.
m = hi/ho
where hi and ho are the image and object heights respectively.
2. For a concave mirror, magnification is always negative (since it is an inverted image).
m = -3
3. Image distance can be calculated using the magnification formula:
m = -v/u
=> -3 = -v/(-10)
=> v = -30 cm
4. Now, we can use the mirror formula to find the focal length of the mirror.
1/f = 1/v + 1/u
=> 1/f = 1/-30 + 1/(-10)
=> 1/f = -1/15
=> f = -15 cm
5. The radius of curvature (R) of the mirror is twice the focal length (f).
R = 2f
=> R = -30 cm
Conclusion:
The radius of curvature of the concave mirror is -30 cm. This means that the mirror has a focal length of -15 cm (since f = R/2).
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A concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror?
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A concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror? 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 concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror?.
A concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror? 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 concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A concave mirror produces there times enlarged image of an object placed at 10 cm in front of it.calculate the radius of curvature of the mirror?.
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