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An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.?
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An object of size 7.0 cm is placed at 27 cm in front of a concave mirr...
**Given:**
Size of object (h) = 7.0 cm
Distance of object (u) = -27 cm (negative sign indicates that the object is placed in front of the mirror)
Focal length of concave mirror (f) = -18 cm (negative sign indicates concave mirror)
**To find:**
1. Distance of the screen (v) from the mirror
2. Size and nature of the image
**Formula used:**
The mirror formula is given by:
1/f = 1/v - 1/u
**Calculation:**
1. Calculate the distance of the screen (v) from the mirror:
Using the mirror formula,
1/f = 1/v - 1/u
Substituting the given values,
1/-18 = 1/v - 1/-27
Simplifying the equation,
1/v = 1/-18 + 1/-27
1/v = -3/54 - 2/54
1/v = -5/54
Taking the reciprocal of both sides,
v = -54/5 cm
Therefore, the distance of the screen from the mirror is -54/5 cm.
2. Calculate the size and nature of the image:
The magnification formula is given by:
magnification (m) = -v/u
Substituting the given values,
m = -(-54/5)/-27
m = 54/5 * 1/27
m = 54/135
Simplifying the fraction,
m = 2/5
Since the magnification is positive, the image formed is erect.
The size of the image (h') can be calculated using the magnification formula:
h' = m * h
Substituting the values,
h' = 2/5 * 7.0
h' = 14/5 cm
Therefore, the size of the image is 14/5 cm and it is erect.
**Summary:**
The distance of the screen from the concave mirror should be -54/5 cm. The size of the image formed is 14/5 cm and it is erect.
Size of object (h) = 7.0 cm
Distance of object (u) = -27 cm (negative sign indicates that the object is placed in front of the mirror)
Focal length of concave mirror (f) = -18 cm (negative sign indicates concave mirror)
**To find:**
1. Distance of the screen (v) from the mirror
2. Size and nature of the image
**Formula used:**
The mirror formula is given by:
1/f = 1/v - 1/u
**Calculation:**
1. Calculate the distance of the screen (v) from the mirror:
Using the mirror formula,
1/f = 1/v - 1/u
Substituting the given values,
1/-18 = 1/v - 1/-27
Simplifying the equation,
1/v = 1/-18 + 1/-27
1/v = -3/54 - 2/54
1/v = -5/54
Taking the reciprocal of both sides,
v = -54/5 cm
Therefore, the distance of the screen from the mirror is -54/5 cm.
2. Calculate the size and nature of the image:
The magnification formula is given by:
magnification (m) = -v/u
Substituting the given values,
m = -(-54/5)/-27
m = 54/5 * 1/27
m = 54/135
Simplifying the fraction,
m = 2/5
Since the magnification is positive, the image formed is erect.
The size of the image (h') can be calculated using the magnification formula:
h' = m * h
Substituting the values,
h' = 2/5 * 7.0
h' = 14/5 cm
Therefore, the size of the image is 14/5 cm and it is erect.
**Summary:**
The distance of the screen from the concave mirror should be -54/5 cm. The size of the image formed is 14/5 cm and it is erect.
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An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.?
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An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature 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 An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.?.
An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature 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 An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focused image can be obtained? Find the size and the nature of the image.?.
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