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How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object?
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How far should one hold an object from a concave mirror of focal lengt...
Answer
In order to find the distance of an object from a concave mirror to get a virtual image twice the size of the object, we need to use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the distance of the image from the mirror
- u is the distance of the object from the mirror
Determine the required values
As per the problem statement, the focal length of the mirror is 40 cm. Let's assume that the distance of the object from the mirror is u cm and the distance of the image from the mirror is v cm.
Given that the virtual image is twice the size of the object, we can write:
magnification = height of image / height of object = 2
Since the image is virtual, its height is negative, while the height of the object is positive. Therefore, we can write:
magnification = -v / u = 2
Solving for v, we get:
v = -2u
Substitute the values in mirror formula
Now, we can substitute the values of f and v in the mirror formula to get:
1/40 = 1/-2u - 1/u
Simplifying the equation, we get:
-u/20 = 1/-2u
Cross multiplying, we get:
-2u^2 = 20u
Simplifying further, we get:
u = -10 cm
Since the distance of the object from the mirror cannot be negative, we can take the absolute value and write:
u = 10 cm
Final Answer
Therefore, the object should be held at a distance of 10 cm from the concave mirror to get a virtual image twice the size of the object.
Community Answer
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How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object?
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How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object? 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 How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object?.
How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object? 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 How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How far should one hold an object from a concave mirror of focal length 40 cm so as to her a virtual image twice the size of the object?.
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