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A convex lens of focal length 24 cms is placed 12 cms in front of a convex mirror. It is found that when a pin is placed 36 cms in front of the lens, it coincides with its own inverted image formed by the lens and the mirror.Then the focal length of the mirror is
- a)15 cm
- b)30 cm
- c)45 cm
- d)60 cm
Correct answer is option 'B'. Can you explain this answer?
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A convex lens of focal length 24 cms is placed 12 cms in front of a co...
A convex lens of focal length 24 cm is placed 12 cm in front of a convex mirror. It is found that when a pin is placed 36 cm in front of the lens, it coincides with its own inverted image formed by the lens and the mirror. Then the focal length of the mirror is 30 cm.
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A convex lens of focal length 24 cms is placed 12 cms in front of a co...
Given:
- Focal length of the convex lens, f = 24 cm
- Distance of the convex lens from the convex mirror, d = 12 cm
- Distance of the object from the lens, u = 36 cm
To find:
The focal length of the convex mirror.
Explanation:
To solve this problem, we can use the mirror formula for the convex lens along with the lens formula.
1. Mirror Formula:
The mirror formula for the convex lens is given by:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Where,
- f is the focal length of the lens
- v is the image distance
- u is the object distance
2. Lens Formula:
The lens formula for the convex lens is given by:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Where,
- f is the focal length of the lens
- v is the image distance
- u is the object distance
3. Applying the formulas:
Given that the object distance (u) is 36 cm, and the distance of the lens from the mirror (d) is 12 cm.
For the convex lens:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{24} = \frac{1}{v} - \frac{1}{36}$
Simplifying the equation, we get:
$\frac{1}{v} = \frac{1}{24} + \frac{1}{36}$
$\frac{1}{v} = \frac{3+2}{72}$
$\frac{1}{v} = \frac{5}{72}$
$v = \frac{72}{5}$
v = 14.4 cm
Now, we can find the image distance (v') formed by the convex mirror.
For the convex mirror:
$\frac{1}{f'} = \frac{1}{v'} - \frac{1}{u}$
Since the object distance (u) and the image distance (v) are the same, we can substitute the values:
$\frac{1}{f'} = \frac{1}{14.4} - \frac{1}{36}$
$\frac{1}{f'} = \frac{1}{14.4} - \frac{1}{36}$
$\frac{1}{f'} = \frac{5-2}{72}$
$\frac{1}{f'} = \frac{3}{72}$
$f' = \frac{72}{3}$
f' = 24 cm
Therefore, the focal length of the convex mirror is 24 cm, which corresponds to option B.
- Focal length of the convex lens, f = 24 cm
- Distance of the convex lens from the convex mirror, d = 12 cm
- Distance of the object from the lens, u = 36 cm
To find:
The focal length of the convex mirror.
Explanation:
To solve this problem, we can use the mirror formula for the convex lens along with the lens formula.
1. Mirror Formula:
The mirror formula for the convex lens is given by:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Where,
- f is the focal length of the lens
- v is the image distance
- u is the object distance
2. Lens Formula:
The lens formula for the convex lens is given by:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Where,
- f is the focal length of the lens
- v is the image distance
- u is the object distance
3. Applying the formulas:
Given that the object distance (u) is 36 cm, and the distance of the lens from the mirror (d) is 12 cm.
For the convex lens:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{24} = \frac{1}{v} - \frac{1}{36}$
Simplifying the equation, we get:
$\frac{1}{v} = \frac{1}{24} + \frac{1}{36}$
$\frac{1}{v} = \frac{3+2}{72}$
$\frac{1}{v} = \frac{5}{72}$
$v = \frac{72}{5}$
v = 14.4 cm
Now, we can find the image distance (v') formed by the convex mirror.
For the convex mirror:
$\frac{1}{f'} = \frac{1}{v'} - \frac{1}{u}$
Since the object distance (u) and the image distance (v) are the same, we can substitute the values:
$\frac{1}{f'} = \frac{1}{14.4} - \frac{1}{36}$
$\frac{1}{f'} = \frac{1}{14.4} - \frac{1}{36}$
$\frac{1}{f'} = \frac{5-2}{72}$
$\frac{1}{f'} = \frac{3}{72}$
$f' = \frac{72}{3}$
f' = 24 cm
Therefore, the focal length of the convex mirror is 24 cm, which corresponds to option B.
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A convex lens of focal length 24 cms is placed 12 cms in front of a convex mirror. It is found that when a pin is placed 36 cms in front of the lens, it coincides with its own inverted image formed by the lens and the mirror.Then the focal length of the mirror isa)15 cmb)30 cmc)45 cmd)60 cmCorrect answer is option 'B'. Can you explain this answer?
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A convex lens of focal length 24 cms is placed 12 cms in front of a convex mirror. It is found that when a pin is placed 36 cms in front of the lens, it coincides with its own inverted image formed by the lens and the mirror.Then the focal length of the mirror isa)15 cmb)30 cmc)45 cmd)60 cmCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A convex lens of focal length 24 cms is placed 12 cms in front of a convex mirror. It is found that when a pin is placed 36 cms in front of the lens, it coincides with its own inverted image formed by the lens and the mirror.Then the focal length of the mirror isa)15 cmb)30 cmc)45 cmd)60 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A convex lens of focal length 24 cms is placed 12 cms in front of a convex mirror. It is found that when a pin is placed 36 cms in front of the lens, it coincides with its own inverted image formed by the lens and the mirror.Then the focal length of the mirror isa)15 cmb)30 cmc)45 cmd)60 cmCorrect answer is option 'B'. Can you explain this answer?.
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