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A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?
- a)10 cm
- b)15 cm
- c)20 cm
- d)25 cm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A point object is placed at a distance of 12 cm on the axis of a conve...
The incident ray OA is refracted along BD by the lens. Singe the image coincides with the object. the refracted ray BD must retrace its path after reflection from the mirror, i.e., it falls normally on the mirror.
Let C be the point on the axis where BD produced meets the axis. It is clear that C is the centre of curvature of the mirror. Also is the imago of the object O formed by the lens alone. Thus
f = +10 cm and u = - 12 cm
The distance v of the image is obtained from the lens formula
Let C be the point on the axis where BD produced meets the axis. It is clear that C is the centre of curvature of the mirror. Also is the imago of the object O formed by the lens alone. Thus
f = +10 cm and u = - 12 cm
The distance v of the image is obtained from the lens formula
which gives v = - 60 cm
Since x = 10 cm. R = v - x = 60 - 10 = 50 cm.
Since x = 10 cm. R = v - x = 60 - 10 = 50 cm.
Hence, the focal length of the mirror = R/2 = 25cm
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A point object is placed at a distance of 12 cm on the axis of a conve...
Given data:
Distance of the point object from the convex lens, u1 = 12 cm
Focal length of the convex lens, f1 = 10 cm
Distance of the convex mirror from the convex lens, u2 = 10 cm
To find: Focal length of the convex mirror, f2
Applying the lens formula for the convex lens:
1/f1 = 1/v1 - 1/u1
Since the image formed by the combination coincides with the object itself, the image formed by the convex lens will act as the object for the convex mirror.
Therefore, the distance of the image formed by the convex lens, v1 = -u1
Substituting the values, we get:
1/f1 = 1/-u1 - 1/u1
1/f1 = -2/u1
f1 = -u1/2
Since the focal length of a convex lens is positive, we take the absolute value:
f1 = u1/2
f1 = 12/2
f1 = 6 cm
Now, applying the mirror formula for the convex mirror:
1/f2 = 1/v2 - 1/u2
Since the image formed by the convex lens acts as the object for the convex mirror, the distance of the object for the convex mirror, u2 = -v1
Substituting the values, we get:
1/f2 = 1/-v1 - 1/u2
1/f2 = -1/u1 - 1/u2
1/f2 = -1/12 - 1/10
1/f2 = (-5 - 6)/60
1/f2 = -11/60
Taking the reciprocal of both sides to find f2, we get:
f2 = -60/11
Since the focal length of a convex mirror is positive, we take the absolute value:
f2 = 60/11
f2 ≈ 5.45 cm
Therefore, the focal length of the convex mirror is approximately 5.45 cm, which is closest to option D) 25 cm.
Distance of the point object from the convex lens, u1 = 12 cm
Focal length of the convex lens, f1 = 10 cm
Distance of the convex mirror from the convex lens, u2 = 10 cm
To find: Focal length of the convex mirror, f2
Applying the lens formula for the convex lens:
1/f1 = 1/v1 - 1/u1
Since the image formed by the combination coincides with the object itself, the image formed by the convex lens will act as the object for the convex mirror.
Therefore, the distance of the image formed by the convex lens, v1 = -u1
Substituting the values, we get:
1/f1 = 1/-u1 - 1/u1
1/f1 = -2/u1
f1 = -u1/2
Since the focal length of a convex lens is positive, we take the absolute value:
f1 = u1/2
f1 = 12/2
f1 = 6 cm
Now, applying the mirror formula for the convex mirror:
1/f2 = 1/v2 - 1/u2
Since the image formed by the convex lens acts as the object for the convex mirror, the distance of the object for the convex mirror, u2 = -v1
Substituting the values, we get:
1/f2 = 1/-v1 - 1/u2
1/f2 = -1/u1 - 1/u2
1/f2 = -1/12 - 1/10
1/f2 = (-5 - 6)/60
1/f2 = -11/60
Taking the reciprocal of both sides to find f2, we get:
f2 = -60/11
Since the focal length of a convex mirror is positive, we take the absolute value:
f2 = 60/11
f2 ≈ 5.45 cm
Therefore, the focal length of the convex mirror is approximately 5.45 cm, which is closest to option D) 25 cm.
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A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer?
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A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 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 A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 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 A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer?.
A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 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 A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 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 A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer?.
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A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?a)10 cmb)15 cmc)20 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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