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Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and the mirror?
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Size of image of an object formed by a mirror having a focal length of...
1/f= 1/v +1/u .
=> -1/20 = 3/u + 1/ u= 4/u
therefore.u = -80 cm.
CASE 2 :-
M = +1/3 (IN CASE OF CONVEX MIRROR)
f=+20 cm.
m=+1/3 =-v/u
v=-u/3.
i/f=1/v+1/u.
=> 1/20= -3/4 + 1/4 =-2/4
therefore, u= -40 cm.
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Most Upvoted Answer
Size of image of an object formed by a mirror having a focal length of...
Given data:
- Focal length of the mirror (f) = 20 cm
- Size of the image (h') = 1/3 times the size of the object (h)
Formula:
The magnification of an image formed by a mirror is given by the formula:
M = -h'/h
Calculation:
Given that the size of the image is reduced to 1/3rd of the size of the object, we can write:
1/3 = -h'/h
Simplifying the equation, we get:
h'/h = -1/3
This implies that the magnification of the image is -1/3.
Nature of the Image:
When the magnification of an image is negative, it means that the image formed is virtual and upright. In this case, the negative sign indicates that the image is inverted.
Nature of the Mirror:
Since the image is virtual and upright, it means that the mirror is a convex mirror. Convex mirrors always produce virtual and upright images.
Distance of the Object:
To find the distance of the object from the mirror (u), we can use the mirror formula:
1/f = 1/u + 1/v
Since the focal length (f) is given as 20 cm, we can substitute the values in the formula and solve for u.
1/20 = 1/u + 1/v
Since the image formed is virtual, the image distance (v) is negative. Let's assume the distance of the object from the mirror (u) as 'd'.
1/20 = 1/d + 1/-d/3
Simplifying the equation, we get:
1/20 = (3-d)/3d
Cross-multiplying, we have:
3d = 60 - 20d
Bringing all the terms to one side, we get:
3d + 20d = 60
23d = 60
Dividing both sides by 23, we get:
d = 60/23 cm
Therefore, the object has been placed at a distance of approximately 2.61 cm from the convex mirror.
- Focal length of the mirror (f) = 20 cm
- Size of the image (h') = 1/3 times the size of the object (h)
Formula:
The magnification of an image formed by a mirror is given by the formula:
M = -h'/h
Calculation:
Given that the size of the image is reduced to 1/3rd of the size of the object, we can write:
1/3 = -h'/h
Simplifying the equation, we get:
h'/h = -1/3
This implies that the magnification of the image is -1/3.
Nature of the Image:
When the magnification of an image is negative, it means that the image formed is virtual and upright. In this case, the negative sign indicates that the image is inverted.
Nature of the Mirror:
Since the image is virtual and upright, it means that the mirror is a convex mirror. Convex mirrors always produce virtual and upright images.
Distance of the Object:
To find the distance of the object from the mirror (u), we can use the mirror formula:
1/f = 1/u + 1/v
Since the focal length (f) is given as 20 cm, we can substitute the values in the formula and solve for u.
1/20 = 1/u + 1/v
Since the image formed is virtual, the image distance (v) is negative. Let's assume the distance of the object from the mirror (u) as 'd'.
1/20 = 1/d + 1/-d/3
Simplifying the equation, we get:
1/20 = (3-d)/3d
Cross-multiplying, we have:
3d = 60 - 20d
Bringing all the terms to one side, we get:
3d + 20d = 60
23d = 60
Dividing both sides by 23, we get:
d = 60/23 cm
Therefore, the object has been placed at a distance of approximately 2.61 cm from the convex mirror.
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Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and the mirror?
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Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and 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 Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and the mirror? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and the mirror?.
Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and 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 Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and the mirror? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Size of image of an object formed by a mirror having a focal length of 20cm is observed to be reduced to 1/3rd of it's size .At what distance , the object has been placed from the mirror? What is the nature of the image and the mirror?.
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