Concept explainers
Figure P26.72 shows a thin converging lens for which the radii of curvature of its surfaces have magnitudes of 9.00 cm and 11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm. Assume the focal points F1 and F2 of the lens are 5.00 cm from the center of the lens. (a) Determine the index of refraction of the lens material. The lens and mirror are 20.0 cm apart, and an object is placed 8.00 cm to the left of the lens. Determine (b) the position of the final image and (c) its magnification as seen by the eye in the figure. (d) Is the final image inverted or upright? Explain.
(a)
Refractive index of the lens material.
Answer to Problem 72P
Refractive index is
Explanation of Solution
Write down the Lens- maker’s equation.
Here
Rearrange (I) in terms of
Conclusion:
Substitute
Refractive index is
(b)
Position of the final image.
Answer to Problem 72P
The final image is real
The image is
Explanation of Solution
Write the thin lens equation
Here
Rewrite (III) in terms of
Write the equation for image magnification.
The image becomes the object for the concave mirror.
Then,
Here
Write the equation for focal length
Here
Write the equation for
Write the equation for image magnification
The image formed by the mirror serves as real object for the lens on the second pass.
Then the image distance will be
Write the equation for image magnification for this case
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The final image is real
The image is
(c)
Overall magnification of the image
Answer to Problem 72P
Overall magnification is
Explanation of Solution
Write the equation for overall magnification
Here
Conclusion:
Substitute
(d)
Whether the image is upright or inverted.
Answer to Problem 72P
The image is inverted.
Explanation of Solution
Sign of magnification decides whether the image is upright or inverted.
If magnification is positive, image is upright. If magnification is negative the image s inverted
Conclusion:
As the overall magnification is
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Chapter 26 Solutions
Principles of Physics: A Calculus-Based Text
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