Concept explainers
A diverging lens has a focal length of magnitude 20.0 cm. (a) Locate the image for object distances of (i) 40.0 cm, (ii) 20.0 cm, and (iii) 10.0 cm. For each case, state whether the image is (b) real or virtual and (c) upright or inverted.(d) For each case, find the magnification.
(a)
The location of the image for given object distance.
Answer to Problem 36.46P
The location of the image for an object distance of (i)
Explanation of Solution
Given: The magnitude of the focal length of the lens is
Write the equation for lens.
Here,
The focal length is negative for diverging lens. The value of focal length is
For case (i), the object distance is
Substitute
Thus, the location of the image for an object distance of
For case (ii), the object distance is
Substitute
Thus, the location of the image for an object distance of
For case (iii), the object distance is
Substitute
The location of the image for an object distance of
Conclusion:
Therefore, the location of the image for an object distance of (i)
(b)
Whether the image for the given object distance is real or virtual.
Answer to Problem 36.46P
The image for an object distance of (i)
Explanation of Solution
Given: The magnitude of the focal length of the lens is
The image is real when the image distance is positive
From the calculation of part (a) in case (i), the image distance is,
Thus, the image distance is
From the calculation of part (a) in case (ii), the image distance is,
Thus, the image distance is
From the calculation of part (a) in case (iii), the image distance is,
The image distance is
Conclusion:
Therefore, the image for an object distance of (i)
(c)
Whether the image for the given object distance is upright or inverted.
Answer to Problem 36.46P
The image for an object distance of (i)
Explanation of Solution
Given: The magnitude of the focal length of the lens is
Write the equation for magnification of the image.
Here,
The image is upright when the magnification is positive
For case (i), the object distance is
Substitute
The magnification is
For case (ii), the object distance is
Substitute
The magnification is
For case (iii), the object distance is
Substitute
The magnification is
Conclusion:
Therefore, the image for an object distance of (i)
(d)
The magnification for the given object distance.
Answer to Problem 36.46P
The magnification for an object distance of (i)
Explanation of Solution
Given: The magnitude of the focal length of the lens is
From the calculation of part (c) in case (i), the magnification for an object distance of
Thus, the magnification is
From the calculation of part (c) in case (ii), the magnification for an object distance of
Thus, the magnification is
From the calculation of part (c) in case (iii), the magnification for an object distance of
The magnification is
Conclusion:
Therefore, the magnification for an object distance of (i)
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Chapter 36 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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