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At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.?
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Given Data
- Focal length of the concave lens (f) = -20 cm (negative for concave)
- Height of the object (h) = 6 cm
- Image distance (v) = -15 cm (negative for virtual images)
Finding Object Distance
To find the object distance (u), we will use the lens formula:
1/f = 1/v + 1/u
Substituting the values:
1/-20 = 1/-15 + 1/u
Rearranging gives:
1/u = 1/-20 - 1/-15
To find a common denominator (60):
1/u = -3/60 + 4/60 = 1/60
Thus, u = 60 cm.
Conclusion on Object Placement
- The object should be placed at a distance of 60 cm from the concave lens.
Calculating the Size of the Image
To calculate the size of the image (h'), we can use the magnification formula:
Magnification (m) = h'/h = -v/u
Substituting the values:
m = -(-15)/(-60) = 15/60 = 1/4
Now substituting back to find h':
h' = m * h = (1/4) * 6 cm = 1.5 cm
Final Image Size
- The size of the image formed will be 1.5 cm tall.
Summary
- Object Distance: 60 cm
- Image Size: 1.5 cm tall
This setup allows for a virtual image that is smaller than the object, typical of concave lenses.
- Focal length of the concave lens (f) = -20 cm (negative for concave)
- Height of the object (h) = 6 cm
- Image distance (v) = -15 cm (negative for virtual images)
Finding Object Distance
To find the object distance (u), we will use the lens formula:
1/f = 1/v + 1/u
Substituting the values:
1/-20 = 1/-15 + 1/u
Rearranging gives:
1/u = 1/-20 - 1/-15
To find a common denominator (60):
1/u = -3/60 + 4/60 = 1/60
Thus, u = 60 cm.
Conclusion on Object Placement
- The object should be placed at a distance of 60 cm from the concave lens.
Calculating the Size of the Image
To calculate the size of the image (h'), we can use the magnification formula:
Magnification (m) = h'/h = -v/u
Substituting the values:
m = -(-15)/(-60) = 15/60 = 1/4
Now substituting back to find h':
h' = m * h = (1/4) * 6 cm = 1.5 cm
Final Image Size
- The size of the image formed will be 1.5 cm tall.
Summary
- Object Distance: 60 cm
- Image Size: 1.5 cm tall
This setup allows for a virtual image that is smaller than the object, typical of concave lenses.
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At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.?
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At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.?.
At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what distance from a concave lens of focal length 20cm a 6 cm tall object be placed so as to obtain it's image at 15cm from the lens? Also calculate the size of the image formed.?.
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