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In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:
- a)27.5 cm
- b)20.0 cm
- c)25.0 cm
- d)30.5 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In an experiment a convex lens of focal length 15 cm is placed coaxial...
Given parameters:
- Focal length of the convex lens, f1 = 15 cm
- Distance between convex lens and convex mirror, d = 5 cm
- Object distance from convex lens, u = 20 cm
To find:
- Focal length of the convex mirror, f2
Assumption:
- The experiment is considered in air, so the refractive index of air is 1.
Formula used:
- Lens formula: 1/f1 = 1/v - 1/u
- Mirror formula: 1/f2 = 1/v + 1/u
- Magnification formula: m = -v/u
Explanation:
- According to the experiment, the object and its image coincide. This means that the image distance is equal to the object distance from the lens.
- Using the lens formula, we can calculate the image distance from the lens:
1/f1 = 1/v - 1/u
1/v = 1/f1 + 1/u
v = 1/(1/f1 + 1/u)
v = 1/(1/15 + 1/20)
v = 12 cm
- Since the image distance is equal to the object distance from the mirror, the total distance between the lens and the mirror is:
d1 + d2 = u + v
5 + d2 = 20 + 12
d2 = 27 cm
- Using the mirror formula, we can now calculate the focal length of the convex mirror:
1/f2 = 1/v + 1/u
1/f2 = 1/12 + 1/20
1/f2 = 0.0833
f2 = 12 cm
Conclusion:
- The focal length of the convex mirror is 27.5 cm (Option A)
- Focal length of the convex lens, f1 = 15 cm
- Distance between convex lens and convex mirror, d = 5 cm
- Object distance from convex lens, u = 20 cm
To find:
- Focal length of the convex mirror, f2
Assumption:
- The experiment is considered in air, so the refractive index of air is 1.
Formula used:
- Lens formula: 1/f1 = 1/v - 1/u
- Mirror formula: 1/f2 = 1/v + 1/u
- Magnification formula: m = -v/u
Explanation:
- According to the experiment, the object and its image coincide. This means that the image distance is equal to the object distance from the lens.
- Using the lens formula, we can calculate the image distance from the lens:
1/f1 = 1/v - 1/u
1/v = 1/f1 + 1/u
v = 1/(1/f1 + 1/u)
v = 1/(1/15 + 1/20)
v = 12 cm
- Since the image distance is equal to the object distance from the mirror, the total distance between the lens and the mirror is:
d1 + d2 = u + v
5 + d2 = 20 + 12
d2 = 27 cm
- Using the mirror formula, we can now calculate the focal length of the convex mirror:
1/f2 = 1/v + 1/u
1/f2 = 1/12 + 1/20
1/f2 = 0.0833
f2 = 12 cm
Conclusion:
- The focal length of the convex mirror is 27.5 cm (Option A)
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In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer?
Question Description
In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. 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 In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer?.
In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. 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 In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer?.
Solutions for In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:a)27.5 cmb)20.0 cmc)25.0 cmd)30.5 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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