Concept explainers
(a)
The ray diagram for the two locations.
(a)
Explanation of Solution
Introduction:
The ray diagram is related to show the focal length
Draw a ray diagram to show the position of object, image and screen.
Conclusion:
Thus, the ray diagram is given above.
(b)
The focal length of the lens using Bessel’s equation.
(b)
Explanation of Solution
Given:
The object to image distance is
The distance between the two position of the lens is
Formula used:
Write the expression for focal length using Bessel’s method.
Here,
Calculation:
Substitute
Conclusion:
Thus, the focal length of the lens is
(c)
The two locations of the lens with respect to the object
(c)
Explanation of Solution
Given:
The object to image distance is
The distance between the two position of the lens is
Formula used:
Write the expression for the first lens equation.
Here,
Write the expression for the second lens equation.
Here,
Write the expression for the distance between object and screen for first lens.
Here,
Write the expression for the distance between object and screen for first lens.
Write the distance between the two lenses in terms of first image.
Here,
Write the distance between the two lenses in terms of second image.
Calculation:
Subtract equation (3) from equation (2).
Substitute
Rearrange the above equation.
Substitute
Add equation (3) to equation (2).
Substitute
Rearrange the above equation.
Substitute
Conclusion:
Thus, the two locations of the lens with respect to object are
(d)
The magnification of the images for two different positions of the lens.
(d)
Explanation of Solution
Given:
The object to image distance is
The distance between the two position of the lens is
The distance of the first object is
The distance of the second object is
Formula used:
Write the expression for the distance between object and screen for first lens.
Here,
Rearrange the above equation.
Write the expression for the distance between object and screen for first lens.
Rearrange the above equation.
Write the expression for the lateral magnification of the first image.
Here,
Write the expression for the lateral magnification of the second image.
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the magnification of the two images for two lens positions are
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Chapter 32 Solutions
Physics for Scientists and Engineers
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