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The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came?
Most Upvoted Answer
The linear magnification for a mirror is the ratio of the size of the ...
Mirror equation is,
1/v + 1/u = 1/f
Now multiply throughout with "u",
u/v + 1 = u/f
Given, I/O = v/u = m
1/m = u/f - 1 = (u - f) /f
=> m = f/(u - f)
1/v + 1/u = 1/f
Now multiply throughout with "u",
u/v + 1 = u/f
Given, I/O = v/u = m
1/m = u/f - 1 = (u - f) /f
=> m = f/(u - f)
Community Answer
The linear magnification for a mirror is the ratio of the size of the ...
Linear Magnification in Mirrors
Linear magnification is an important concept in mirrors and is denoted by the symbol m. It is defined as the ratio of the size of the image to the size of the object. In other words, it tells us how much larger or smaller the image is compared to the object.
Formula for Magnification
The magnitude of the linear magnification can be calculated using the following formula:
m = size of image / size of object
Proof of the Formula
To understand how the formula for magnification is derived, let's consider a concave mirror with a focal length of f. Let the object be placed at a distance u from the mirror and the image be formed at a distance v from the mirror.
From the mirror formula, we know that:
1/f = 1/u + 1/v
Solving for v, we get:
v = uf / (u - f)
Now, the magnification is given by:
m = size of image / size of object
Let the height of the object be h and the height of the image be h'. Then, we can write:
m = h' / h
Using the mirror formula, we can also show that:
h' / h = -v / u
Substituting the value of v, we get:
h' / h = -uf / (u - f) * 1/u
Simplifying, we get:
h' / h = -f / (u - f)
Therefore, the magnitude of the linear magnification is:
m = size of image / size of object = h' / h = -f / (u - f)
Final Answer
Therefore, the correct option is (C) f / (u - f).
Linear magnification is an important concept in mirrors and is denoted by the symbol m. It is defined as the ratio of the size of the image to the size of the object. In other words, it tells us how much larger or smaller the image is compared to the object.
Formula for Magnification
The magnitude of the linear magnification can be calculated using the following formula:
m = size of image / size of object
Proof of the Formula
To understand how the formula for magnification is derived, let's consider a concave mirror with a focal length of f. Let the object be placed at a distance u from the mirror and the image be formed at a distance v from the mirror.
From the mirror formula, we know that:
1/f = 1/u + 1/v
Solving for v, we get:
v = uf / (u - f)
Now, the magnification is given by:
m = size of image / size of object
Let the height of the object be h and the height of the image be h'. Then, we can write:
m = h' / h
Using the mirror formula, we can also show that:
h' / h = -v / u
Substituting the value of v, we get:
h' / h = -uf / (u - f) * 1/u
Simplifying, we get:
h' / h = -f / (u - f)
Therefore, the magnitude of the linear magnification is:
m = size of image / size of object = h' / h = -f / (u - f)
Final Answer
Therefore, the correct option is (C) f / (u - f).
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The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came?
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The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came? 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 The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came?.
The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came? 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 The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The linear magnification for a mirror is the ratio of the size of the image to the size of object, and is denoted by m. Then magnitude of m is equal to(symbol there usual meaning) (A) uf/(u-f) (B) uf/(u-f) (C) f/(u-f) (D) none of these and proof that how it came?.
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