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An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?
- a)6cm
- b)30cm
- c)both (1) and (2)
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
An object is placed at 30 cm from a convex lens of focal length 15cm. ...
For image to be coincident, either the rays should retrace or the image due to the lens should formed just at the pole of the mirror in thin case. The image formed due to lens is at 30 cm (2f) be from the lens. Thus either this image should be at centre of curvature of the convex mirroror at the pole of the mirror. Hence 6cm or 30cm should be the separation between the lens and the mirror.
Most Upvoted Answer
An object is placed at 30 cm from a convex lens of focal length 15cm. ...
Given Information:
- Distance of the object from the convex lens (d1) = 30 cm
- Focal length of the convex lens (f1) = 15 cm
- Focal length of the convex mirror (f2) = 12 cm
Objective:
To find the separation between the lens and mirror.
Autocollimation:
Autocollimation is a phenomenon in which the object and the image coincide or overlap. In this case, the object is placed at a distance such that the lens and mirror combination form an image of the object at the same position as the object itself.
Analysis:
1. The lens formula relates the object distance (u), image distance (v), and the focal length (f) of a lens as:
1/f = 1/v - 1/u
2. For the convex lens, the focal length is positive. So, using the lens formula, we can determine the image distance (v1) formed by the convex lens.
3. The image formed by the convex lens acts as a virtual object for the convex mirror. The image distance (u2) for the convex mirror is equal to the image distance (v1) of the convex lens.
4. Using the mirror formula, we can determine the image distance (v2) formed by the convex mirror.
5. Since the object and image coincide, the image distance (v2) is equal to the object distance (u2).
Calculation:
1. For the convex lens:
1/f1 = 1/v1 - 1/u1
1/15 = 1/v1 - 1/30
2/v1 = 1/15
v1 = 30 cm
2. For the convex mirror:
1/f2 = 1/v2 - 1/u2
1/12 = 1/30 - 1/u2
1/u2 = 1/12 - 1/30
u2 = 30/5 - 30/12
u2 = 6 - 2.5
u2 = 3.5 cm
3. Since the object and image coincide, v2 = u2
Therefore, the separation between the lens and mirror = u2 - v1
Separation = 3.5 - 30
Separation = -26.5 cm
Conclusion:
The separation between the lens and mirror is -26.5 cm. However, a negative distance does not make physical sense in this context. Therefore, the separation between the lens and mirror is 26.5 cm.
- Distance of the object from the convex lens (d1) = 30 cm
- Focal length of the convex lens (f1) = 15 cm
- Focal length of the convex mirror (f2) = 12 cm
Objective:
To find the separation between the lens and mirror.
Autocollimation:
Autocollimation is a phenomenon in which the object and the image coincide or overlap. In this case, the object is placed at a distance such that the lens and mirror combination form an image of the object at the same position as the object itself.
Analysis:
1. The lens formula relates the object distance (u), image distance (v), and the focal length (f) of a lens as:
1/f = 1/v - 1/u
2. For the convex lens, the focal length is positive. So, using the lens formula, we can determine the image distance (v1) formed by the convex lens.
3. The image formed by the convex lens acts as a virtual object for the convex mirror. The image distance (u2) for the convex mirror is equal to the image distance (v1) of the convex lens.
4. Using the mirror formula, we can determine the image distance (v2) formed by the convex mirror.
5. Since the object and image coincide, the image distance (v2) is equal to the object distance (u2).
Calculation:
1. For the convex lens:
1/f1 = 1/v1 - 1/u1
1/15 = 1/v1 - 1/30
2/v1 = 1/15
v1 = 30 cm
2. For the convex mirror:
1/f2 = 1/v2 - 1/u2
1/12 = 1/30 - 1/u2
1/u2 = 1/12 - 1/30
u2 = 30/5 - 30/12
u2 = 6 - 2.5
u2 = 3.5 cm
3. Since the object and image coincide, v2 = u2
Therefore, the separation between the lens and mirror = u2 - v1
Separation = 3.5 - 30
Separation = -26.5 cm
Conclusion:
The separation between the lens and mirror is -26.5 cm. However, a negative distance does not make physical sense in this context. Therefore, the separation between the lens and mirror is 26.5 cm.
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An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer?
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An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. 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 An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer?.
An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. 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 An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of An object is placed at 30 cm from a convex lens of focal length 15cm. On the other side of the lens a convex mirror of focal length 12cm is placed so that the principal axis of both coincide. It is observed that the object and image coincide (autocollimation). What is the separation between the lens and mirror?a)6cmb)30cmc)both (1) and (2)d)none of the aboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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