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A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]
- a)10 cm
- b)15 cm
- c)2.5 cm
- d)5 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A rod of length 10 cm lies along the principalaxis of a concave mirror...
The focal length of the mirror
For A end of the rod the image distance
When u1 = – 20 cm
When u1 = – 20 cm
For when u2 = – 30 cm
Most Upvoted Answer
A rod of length 10 cm lies along the principalaxis of a concave mirror...
Given:
Length of the rod = 10 cm
Focal length of the concave mirror = -10 cm (negative sign indicates concave mirror)
To find:
Length of the image formed by the mirror
Formula:
The magnification produced by a concave mirror is given by the formula:
magnification (m) = -v/u
Where,
v = image distance
u = object distance
Using the mirror formula:
1/f = 1/v - 1/u
Since the object is placed at infinity, the formula becomes:
1/f = 1/v
From the given information, we can determine the object distance (u) as follows:
Length of the rod = 10 cm
Distance of the end closer to the pole from the mirror = 20 cm
Distance of the end farther from the mirror = 20 + 10 = 30 cm
Object distance (u) = (20 + 30)/2 = 25 cm
Substituting the values of f and u in the mirror formula:
1/10 = 1/v
Solving for v:
v = 10 cm
Using the formula for magnification:
m = -v/u
m = -10/25
m = -2/5
The negative sign indicates an inverted image.
Length of the image:
Length of the image = magnification x length of the object
Length of the image = (-2/5) x 10
Length of the image = -4 cm (negative sign indicates inversion)
Since the length cannot be negative, we take the magnitude of the length:
Length of the image = | -4 | = 4 cm
Therefore, the length of the image formed by the concave mirror is 4 cm. Hence, option D is the correct answer.
Length of the rod = 10 cm
Focal length of the concave mirror = -10 cm (negative sign indicates concave mirror)
To find:
Length of the image formed by the mirror
Formula:
The magnification produced by a concave mirror is given by the formula:
magnification (m) = -v/u
Where,
v = image distance
u = object distance
Using the mirror formula:
1/f = 1/v - 1/u
Since the object is placed at infinity, the formula becomes:
1/f = 1/v
From the given information, we can determine the object distance (u) as follows:
Length of the rod = 10 cm
Distance of the end closer to the pole from the mirror = 20 cm
Distance of the end farther from the mirror = 20 + 10 = 30 cm
Object distance (u) = (20 + 30)/2 = 25 cm
Substituting the values of f and u in the mirror formula:
1/10 = 1/v
Solving for v:
v = 10 cm
Using the formula for magnification:
m = -v/u
m = -10/25
m = -2/5
The negative sign indicates an inverted image.
Length of the image:
Length of the image = magnification x length of the object
Length of the image = (-2/5) x 10
Length of the image = -4 cm (negative sign indicates inversion)
Since the length cannot be negative, we take the magnitude of the length:
Length of the image = | -4 | = 4 cm
Therefore, the length of the image formed by the concave mirror is 4 cm. Hence, option D is the correct answer.
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A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer?.
A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer?.
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A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A rod of length 10 cm lies along the principalaxis of a concave mirror of focal length 10 cm insuch a way that its end closer to the pole is20 cm away from the mirror. The length of theimage is : [2012M]a)10 cmb)15 cmc)2.5 cmd)5 cmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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