Concept explainers
(a)
The position and size of the image.
(a)
Explanation of Solution
Given:
The height of the object is
The distance of the object in front of a thin lens is
The power of the lens is
Formula used:
Draw a ray diagram to show the position and size of the image.
Write the expression for thin lens equation.
Here,
Write the expression for the focal length in terms of power of a lens.
Here,
Write the expression for lateral magnification in terms of image height and object height.
Here,
Write the expression for lateral magnification in terms of image distance and object distance.
Combine the above two equations.
Calculation:
Substitute
Rewrite equation (1) to calculate the image distance.
Substitute
Substitute
Substitute
Conclusion:
Thus, the image is real and inverted. As the image distance,
(b)
The position and size of the image.
(b)
Explanation of Solution
Given:
The height of the object is
The distance of the object in front of a thin lens is
The power of the lens is
Formula used:
Draw a ray diagram to show the position and size of the image.
Write the expression for thin lens equation.
Write the expression for the focal length in terms of power of a lens.
Write the expression for lateral magnification in terms of image height and object height.
Write the expression for lateral magnification in terms of image distance and object distance.
Combine the above two equations.
Calculation:
Substitute
Rewrite equation (1) to calculate the image distance.
Substitute
Substitute
Substitute
Conclusion:
Thus, the image is real and inverted. As the image distance,
(c)
The position and size of the image.
(c)
Explanation of Solution
Given:
The height of the object is
The distance of the object in front of a thin lens is
The power of the lens is
Formula used:
Draw a ray diagram to show the position and size of the image.
Write the expression for thin lens equation.
Write the expression for the focal length in terms of power of a lens.
Write the expression for lateral magnification in terms of image height and object height.
Write the expression for lateral magnification in terms of image distance and object distance.
Combine the above two equations.
Calculation:
Substitute
Rewrite equation (1) to calculate the image distance.
Substitute
Substitute
Substitute
Conclusion:
Thus, the image is virtual and inverted. As the image distance,
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Chapter 32 Solutions
Physics for Scientists and Engineers, Vol. 3
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