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To form an image twice the size of the object, using a convex lens of focal length 20 cm, the object distance must be –
- a)< 20 cm
- b)> 20 cm
- c)> 20 cm and between 20 cm and 40 cm
- d)Cannot form image
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
To form an image twice the size of the object, using a convex lens of ...
Understanding Convex Lens and Magnification
To determine the object distance for a convex lens to produce an image that is twice the size of the object, we need to apply the lens formula and magnification concepts.
Lens Formula
The lens formula is given by:
1/f = 1/v - 1/u
Where:
- f = focal length of the lens (20 cm)
- v = image distance
- u = object distance
Magnification (m)
Magnification is defined as the ratio of the height of the image (h') to the height of the object (h):
m = h'/h = -v/u
For an image that is twice the size of the object (m = 2), we have:
2 = -v/u
This implies v = -2u.
Finding Object Distance
1. Substitute v in the lens formula:
- f = 20 cm implies 1/20 = 1/v - 1/u
- Replace v with -2u:
1/20 = 1/(-2u) - 1/u
2. Solving leads to:
- Combine the fractions:
1/20 = -1/(2u) + 1/u
- This simplifies to:
1/20 = 1/(2u)
3. Rearranging gives:
- 2u = 20 cm, hence u = 10 cm.
Conclusion on Object Distance
- For the image to be twice the size of the object, the object distance must be:
- Greater than 20 cm and less than 40 cm (option c).
Thus, the correct answer is option 'C'. This indicates that the object must be positioned further than the focal point but not too far, ensuring a larger, virtual image is created.
To determine the object distance for a convex lens to produce an image that is twice the size of the object, we need to apply the lens formula and magnification concepts.
Lens Formula
The lens formula is given by:
1/f = 1/v - 1/u
Where:
- f = focal length of the lens (20 cm)
- v = image distance
- u = object distance
Magnification (m)
Magnification is defined as the ratio of the height of the image (h') to the height of the object (h):
m = h'/h = -v/u
For an image that is twice the size of the object (m = 2), we have:
2 = -v/u
This implies v = -2u.
Finding Object Distance
1. Substitute v in the lens formula:
- f = 20 cm implies 1/20 = 1/v - 1/u
- Replace v with -2u:
1/20 = 1/(-2u) - 1/u
2. Solving leads to:
- Combine the fractions:
1/20 = -1/(2u) + 1/u
- This simplifies to:
1/20 = 1/(2u)
3. Rearranging gives:
- 2u = 20 cm, hence u = 10 cm.
Conclusion on Object Distance
- For the image to be twice the size of the object, the object distance must be:
- Greater than 20 cm and less than 40 cm (option c).
Thus, the correct answer is option 'C'. This indicates that the object must be positioned further than the focal point but not too far, ensuring a larger, virtual image is created.
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Community Answer
To form an image twice the size of the object, using a convex lens of ...
Given, f = 20 cm, h1 = 2h0
⇒ h1/ho = m = 2
v / u = 2 => v = 2u
1/ v - 1/ u = 1/ f ( lens formula)
⇒ 1/2u - 1/-u = 1/ 20
⇒ 3/2u = 1/20
⇒ u = 30 cm
So, option (c) is the correct answer.
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