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Two convex lenses of focal length 10cm and 20cm are kept in contact .The focal length of the combination is:
- a)20/3 cm
- b)40 cm
- c)12cm
- d)15 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two convex lenses of focal length 10cm and 20cm are kept in contact .T...
Focal length of a lens is a measure of its ability to converge or diverge light rays. When two convex lenses are placed in contact, they can be considered as a single lens, and the combined focal length can be determined using the lens formula.
The lens formula is given by:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance
- u is the object distance
To determine the combined focal length of the two lenses, we need to consider their individual focal lengths and the image and object distances.
Let's consider the first lens with a focal length of 10 cm. The image formed by this lens will act as the object for the second lens.
1/f1 = 1/v1 - 1/u1
Since the lenses are in contact, the image distance of the first lens (v1) will be equal to the object distance of the second lens (u2). Therefore, v1 = u2.
Now, let's consider the second lens with a focal length of 20 cm. The image formed by the first lens will act as the object for the second lens.
1/f2 = 1/v2 - 1/u2
Substituting v1 = u2 into the above equation, we get:
1/f2 = 1/v2 - 1/v1
Since the lenses are in contact, the combined focal length (f) can be determined by adding the focal lengths of the individual lenses:
1/f = 1/f1 + 1/f2
Substituting the values of f1 = 10 cm and f2 = 20 cm, we get:
1/f = 1/10 + 1/20
Simplifying the equation:
1/f = 3/30
1/f = 1/10
Therefore, the combined focal length of the two lenses is 10 cm. Hence, the correct answer is option A, 20/3 cm.
The lens formula is given by:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance
- u is the object distance
To determine the combined focal length of the two lenses, we need to consider their individual focal lengths and the image and object distances.
Let's consider the first lens with a focal length of 10 cm. The image formed by this lens will act as the object for the second lens.
1/f1 = 1/v1 - 1/u1
Since the lenses are in contact, the image distance of the first lens (v1) will be equal to the object distance of the second lens (u2). Therefore, v1 = u2.
Now, let's consider the second lens with a focal length of 20 cm. The image formed by the first lens will act as the object for the second lens.
1/f2 = 1/v2 - 1/u2
Substituting v1 = u2 into the above equation, we get:
1/f2 = 1/v2 - 1/v1
Since the lenses are in contact, the combined focal length (f) can be determined by adding the focal lengths of the individual lenses:
1/f = 1/f1 + 1/f2
Substituting the values of f1 = 10 cm and f2 = 20 cm, we get:
1/f = 1/10 + 1/20
Simplifying the equation:
1/f = 3/30
1/f = 1/10
Therefore, the combined focal length of the two lenses is 10 cm. Hence, the correct answer is option A, 20/3 cm.
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Community Answer
Two convex lenses of focal length 10cm and 20cm are kept in contact .T...
Focal length = 10cm and 20cm
power of both lenses = 1/10 diopter and 1/20 diopter
power of combined lenses = 1/10 + 1/20 = 3/20 diopter
so, focal length will reciprocal of power
= 20/3 cm
power of both lenses = 1/10 diopter and 1/20 diopter
power of combined lenses = 1/10 + 1/20 = 3/20 diopter
so, focal length will reciprocal of power
= 20/3 cm
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Two convex lenses of focal length 10cm and 20cm are kept in contact .The focal length of the combination is: a)20/3 cm b)40 cm c)12cm d)15 cm Correct answer is option 'A'. Can you explain this answer?
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