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A convex lens of focal length 15cm is used to form an image of the size of the object .Where from the lens should the object be placed ?
- a)15 cm
- b)30 cm
- c)60 cm
- d)10 cm
Correct answer is option 'B'. Can you explain this answer?
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A convex lens of focal length 15cm is used to form an image of the si...
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Given:
Focal length of convex lens, f = 15 cm
To find:
Where from the lens should the object be placed?
Solution:
To find where the object should be placed, we can use the lens formula:
1/f = 1/v - 1/u
Where,
f = focal length of the lens
v = image distance
u = object distance
Since the lens is used to form an image of the same size as the object, we can assume the magnification (m) to be 1. The magnification is given by:
m = -v/u
Since m = 1, we have:
1 = -v/u
Case 1: Object placed at infinity (u = ∞)
When the object is placed at infinity, the image distance (v) can be calculated as:
1/f = 1/v
v = f = 15 cm
Case 2: Object placed at 30 cm (u = 30 cm)
When the object is placed at a distance of 30 cm from the lens, the image distance (v) can be calculated as:
1/f = 1/v - 1/u
1/15 = 1/v - 1/30
1/v = 1/15 + 1/30
1/v = (2 + 1)/30
1/v = 3/30
v = 30/3 = 10 cm
Case 3: Object placed at 60 cm (u = 60 cm)
When the object is placed at a distance of 60 cm from the lens, the image distance (v) can be calculated as:
1/f = 1/v - 1/u
1/15 = 1/v - 1/60
1/v = 1/15 + 1/60
1/v = (4 + 1)/60
1/v = 5/60
v = 60/5 = 12 cm
Conclusion:
From the calculations, we can see that when the object is placed at a distance of 30 cm from the lens (option B), the image distance is 10 cm, which satisfies the condition of forming an image of the same size as the object. Therefore, the correct answer is option B.
Focal length of convex lens, f = 15 cm
To find:
Where from the lens should the object be placed?
Solution:
To find where the object should be placed, we can use the lens formula:
1/f = 1/v - 1/u
Where,
f = focal length of the lens
v = image distance
u = object distance
Since the lens is used to form an image of the same size as the object, we can assume the magnification (m) to be 1. The magnification is given by:
m = -v/u
Since m = 1, we have:
1 = -v/u
Case 1: Object placed at infinity (u = ∞)
When the object is placed at infinity, the image distance (v) can be calculated as:
1/f = 1/v
v = f = 15 cm
Case 2: Object placed at 30 cm (u = 30 cm)
When the object is placed at a distance of 30 cm from the lens, the image distance (v) can be calculated as:
1/f = 1/v - 1/u
1/15 = 1/v - 1/30
1/v = 1/15 + 1/30
1/v = (2 + 1)/30
1/v = 3/30
v = 30/3 = 10 cm
Case 3: Object placed at 60 cm (u = 60 cm)
When the object is placed at a distance of 60 cm from the lens, the image distance (v) can be calculated as:
1/f = 1/v - 1/u
1/15 = 1/v - 1/60
1/v = 1/15 + 1/60
1/v = (4 + 1)/60
1/v = 5/60
v = 60/5 = 12 cm
Conclusion:
From the calculations, we can see that when the object is placed at a distance of 30 cm from the lens (option B), the image distance is 10 cm, which satisfies the condition of forming an image of the same size as the object. Therefore, the correct answer is option B.
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A convex lens of focal length 15cm is used to form an image of the size of the object .Where from the lens should the object be placed ?a)15 cmb)30 cmc)60 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer?
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