Concept explainers
(a)
The position of the final image.
(a)
Explanation of Solution
Given:
The focal length of a converging lens is
The separation between the two lenses is
The distance of the object from the converging lens is
Formula used:
Draw a ray diagram to show the final image position and size.
Write the expression for thin lens equation for first image.
Here,
Write the expression for thin lens equation for second image.
Here,
Write the expression for the lateral magnification of image due to converging lens.
Here,
Write the expression for the lateral magnification due to the diverging lens.
Here,
Calculation:
Rewrite equation (1) to calculate the first image distance.
Substitute
Substitute
The distance of the object from diverging lens is calculated below.
Here,
Substitute
Rewrite equation (2) to calculate the second image distance.
Substitute
Substitute
The final distance of the image is calculated below.
Here,
Substitute
Conclusion:
Thus, the distance of the final image is
(b)
Whether the final image is real or virtual and upright or inverted.
(b)
Explanation of Solution
Given:
The distance of the second image is
The lateral magnification of the image due to the converging lens is
The lateral magnification of the image due to the diverging lens is
Formula used:
Write the expression for the overall lateral magnification for the system of two lenses.
Here, is the overall lateral magnification for the system of two lenses.
Calculation:
Substitute
Conclusion:
Thus, the image is virtual and inverted. Because the image distance,
(c)
The overall magnification of the system.
(c)
Explanation of Solution
Given:
The lateral magnification of the image due to the converging lens is
The lateral magnification of the image due to the diverging lens is
Formula used:
Write the expression for the overall lateral magnification for the system of two lenses.
Calculation:
Substitute
Conclusion:
Thus, the overall magnification for the system of two lenses is
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Chapter 32 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
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