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An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror is
- a)15 cm
- b)20 cm
- c)25 cm
- d)30 cm
Correct answer is option 'D'. Can you explain this answer?
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An object placed in front of a concave mirror at a distance of x cm fr...
so f = 30 cm
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An object placed in front of a concave mirror at a distance of x cm fr...
Given:
The object is placed in front of a concave mirror at a distance of x cm from the pole.
The magnification of the image when the object is at this position is 3.
When the object is moved to a distance of (x + 5) cm, the magnification of the image becomes 2.
To find:
The focal length of the mirror.
Assumptions:
1. The magnification of the image is given by the formula: magnification = -v/u, where v is the image distance and u is the object distance.
2. The sign convention used is as follows:
- The object distance (u) is positive for objects placed in front of the mirror.
- The image distance (v) is positive for real images formed on the same side as the object.
- The focal length (f) is positive for concave mirrors.
Let's solve the problem step by step:
1. Given that the magnification when the object is at a distance of x cm is 3.
- Using the magnification formula, we can write: 3 = -v/u
- Since the image is real, the image distance (v) will be positive.
- Hence, we can write: v = -3u
2. When the object is moved to a distance of (x + 5) cm, the magnification becomes 2.
- Using the magnification formula, we can write: 2 = -v/(u + 5)
- Since the image is still real, the image distance (v) will be positive.
- Hence, we can write: v = -2(u + 5)
3. Equating the values of v from both equations:
- -3u = -2(u + 5)
- Solving this equation, we get: u = 10 cm
4. Now, substituting the value of u into the first equation, we can find the value of v:
- v = -3u = -3(10) = -30 cm
5. The focal length (f) can be found using the mirror formula: 1/f = 1/v - 1/u
- Substituting the values of v and u, we get: 1/f = 1/-30 - 1/10
- Solving this equation, we get: f = -30 cm
6. Since the focal length (f) cannot be negative, we take its absolute value:
- f = |-30| = 30 cm
Therefore, the correct answer is option D: 30 cm.
The object is placed in front of a concave mirror at a distance of x cm from the pole.
The magnification of the image when the object is at this position is 3.
When the object is moved to a distance of (x + 5) cm, the magnification of the image becomes 2.
To find:
The focal length of the mirror.
Assumptions:
1. The magnification of the image is given by the formula: magnification = -v/u, where v is the image distance and u is the object distance.
2. The sign convention used is as follows:
- The object distance (u) is positive for objects placed in front of the mirror.
- The image distance (v) is positive for real images formed on the same side as the object.
- The focal length (f) is positive for concave mirrors.
Let's solve the problem step by step:
1. Given that the magnification when the object is at a distance of x cm is 3.
- Using the magnification formula, we can write: 3 = -v/u
- Since the image is real, the image distance (v) will be positive.
- Hence, we can write: v = -3u
2. When the object is moved to a distance of (x + 5) cm, the magnification becomes 2.
- Using the magnification formula, we can write: 2 = -v/(u + 5)
- Since the image is still real, the image distance (v) will be positive.
- Hence, we can write: v = -2(u + 5)
3. Equating the values of v from both equations:
- -3u = -2(u + 5)
- Solving this equation, we get: u = 10 cm
4. Now, substituting the value of u into the first equation, we can find the value of v:
- v = -3u = -3(10) = -30 cm
5. The focal length (f) can be found using the mirror formula: 1/f = 1/v - 1/u
- Substituting the values of v and u, we get: 1/f = 1/-30 - 1/10
- Solving this equation, we get: f = -30 cm
6. Since the focal length (f) cannot be negative, we take its absolute value:
- f = |-30| = 30 cm
Therefore, the correct answer is option D: 30 cm.
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An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror isa)15 cmb)20 cmc)25 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer?
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An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror isa)15 cmb)20 cmc)25 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror isa)15 cmb)20 cmc)25 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror isa)15 cmb)20 cmc)25 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer?.
An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror isa)15 cmb)20 cmc)25 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror isa)15 cmb)20 cmc)25 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror isa)15 cmb)20 cmc)25 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer?.
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