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How far should an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ?
Verified Answer
How far should an object be held from a concave mirror of focal length...
Focal length, f = -40 cm
Suppose a real and magnified image is formed. Let object distance be –u, image distance be –v.
The magnification is given as, m = -v/u = -3
Therefore, v = 3u
Now using mirror formula,
(-1/40) = (-1/v) + (-1/u)
=> 1/40 = 1/3u + 1/u
=> 1/40 = 4/3u
=> u = 53.3 cm
=> v = 159.9cm from the pole of the mirror.
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How far should an object be held from a concave mirror of focal length...
Solution:
Given,
Focal length of concave mirror (f) = -40 cm (negative because it is a concave mirror)
Magnification of the image (m) = 3
We need to find the distance of the object from the mirror (u).
Formula:
The formula for magnification (m) in terms of the distance of object (u) and the distance of the image (v) from the mirror for a concave mirror is:
m = -v/u
The formula for the focal length (f) in terms of the distance of object (u) and the distance of the image (v) from the mirror for a concave mirror is:
1/f = 1/u + 1/v
From the above two equations, we can get the value of v in terms of u and f as follows:
v = -fu/(u-f)
Substituting the values of f and m in the above equation, we get:
v = -120 cm
The negative sign indicates that the image is formed on the same side as that of the object.
Answer:
Therefore, the distance of the object from the concave mirror should be 120 cm so as to get an image magnified 3 times.
Given,
Focal length of concave mirror (f) = -40 cm (negative because it is a concave mirror)
Magnification of the image (m) = 3
We need to find the distance of the object from the mirror (u).
Formula:
The formula for magnification (m) in terms of the distance of object (u) and the distance of the image (v) from the mirror for a concave mirror is:
m = -v/u
The formula for the focal length (f) in terms of the distance of object (u) and the distance of the image (v) from the mirror for a concave mirror is:
1/f = 1/u + 1/v
From the above two equations, we can get the value of v in terms of u and f as follows:
v = -fu/(u-f)
Substituting the values of f and m in the above equation, we get:
v = -120 cm
The negative sign indicates that the image is formed on the same side as that of the object.
Answer:
Therefore, the distance of the object from the concave mirror should be 120 cm so as to get an image magnified 3 times.
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How far should an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ?
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How far should an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ? 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 an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How far should an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ?.
How far should an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ? 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 an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How far should an object be held from a concave mirror of focal length 40 cm so as to get an image magnified 3 times ?.
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