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A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.?
Most Upvoted Answer
A concave mirror produces a real image of half the size of the object ...
Initial obj. dist = -60(real object)
". magnification (m) = -1/2 (as both obj and image are real)
We know , m= -f/(u-f) [f=focal length]
f= -20cm
Now , obj dist = u'
magnification(m')=2 (as image is virtual of real object)
f=-20 cm
We know , m= -f/(u'-f)
2=20/(u'+20)
u'=-10cm
Hence , the obj should at a distance of 10 cm in front of the mirror.
Community Answer
A concave mirror produces a real image of half the size of the object ...
Introduction:
A concave mirror is a mirror with a reflective surface that curves inward. It can produce both real and virtual images depending on the position of the object. In this scenario, we have a concave mirror that produces a real image of half the size of the object when the object is placed at a distance of 60cm in front of it. We need to determine the position of the object to obtain a virtual image that is double the size of the object.
Given information:
- Object distance (u) = -60cm (negative sign indicates that the object is placed in front of the mirror)
- Image distance (v) = ?
- Magnification (m) = -0.5 (negative sign indicates an inverted image)
Determining the image distance:
We can use the mirror formula to determine the image distance (v) using the given object distance (u) and magnification (m).
The mirror formula is given by:
1/f = 1/v - 1/u
Where f is the focal length of the mirror.
Determining the focal length:
To determine the focal length of the mirror, we can use the magnification formula:
m = -v/u
Rearranging the formula, we have:
v = -m * u
Substituting the values, we get:
v = -(-0.5) * (-60cm)
v = 30cm
Therefore, the image distance (v) is 30cm.
Determining the object distance for the desired virtual image:
To obtain a virtual image that is double the size of the object, we need to find the new object distance that will result in a magnification of 2.
m = -v/u
Substituting the values, we get:
2 = -30cm/u
Solving for u, we have:
u = -30cm/2
u = -15cm
Therefore, the object should be placed at a distance of 15cm in front of the concave mirror to obtain the desired virtual image that is double the size of the object.
Conclusion:
To obtain a virtual image that is double the size of the object produced by a concave mirror, the object should be placed at a distance of 15cm in front of the mirror. The mirror formula and magnification formula are used to determine the image distance and object distance based on the given information. By understanding the properties of concave mirrors and applying the relevant formulas, we can accurately determine the position of the object to obtain the desired virtual image.
A concave mirror is a mirror with a reflective surface that curves inward. It can produce both real and virtual images depending on the position of the object. In this scenario, we have a concave mirror that produces a real image of half the size of the object when the object is placed at a distance of 60cm in front of it. We need to determine the position of the object to obtain a virtual image that is double the size of the object.
Given information:
- Object distance (u) = -60cm (negative sign indicates that the object is placed in front of the mirror)
- Image distance (v) = ?
- Magnification (m) = -0.5 (negative sign indicates an inverted image)
Determining the image distance:
We can use the mirror formula to determine the image distance (v) using the given object distance (u) and magnification (m).
The mirror formula is given by:
1/f = 1/v - 1/u
Where f is the focal length of the mirror.
Determining the focal length:
To determine the focal length of the mirror, we can use the magnification formula:
m = -v/u
Rearranging the formula, we have:
v = -m * u
Substituting the values, we get:
v = -(-0.5) * (-60cm)
v = 30cm
Therefore, the image distance (v) is 30cm.
Determining the object distance for the desired virtual image:
To obtain a virtual image that is double the size of the object, we need to find the new object distance that will result in a magnification of 2.
m = -v/u
Substituting the values, we get:
2 = -30cm/u
Solving for u, we have:
u = -30cm/2
u = -15cm
Therefore, the object should be placed at a distance of 15cm in front of the concave mirror to obtain the desired virtual image that is double the size of the object.
Conclusion:
To obtain a virtual image that is double the size of the object produced by a concave mirror, the object should be placed at a distance of 15cm in front of the mirror. The mirror formula and magnification formula are used to determine the image distance and object distance based on the given information. By understanding the properties of concave mirrors and applying the relevant formulas, we can accurately determine the position of the object to obtain the desired virtual image.
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A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.?
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A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.?.
A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A concave mirror produces a real image of half the size of the object placed at 60cm in front of it. Where should the object be placed to obtain the virtual image of double the size of the object.?.
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