Concept explainers
A convex-concave lens has faces of radii 3.0 and 4.0 cm, respectively, and is made of glass of refractive index 1.6. Determine (a) its focal length and (b) the linear magnification of the image when the object is 28 cm from the lens.
(a)
The focal length of a convex-concave lens having faces of radii
Answer to Problem 38SP
Solution:
Explanation of Solution
Given data:
The radius of the convex surface is
The radius of the concave surface is
The refractive index of the material is
Formula used:
Write the Lens maker’s equation for a spherical lens.
Here,
Explanation:
Consider the Lens maker’s equation for a spherical lens.
Substitute
Solve for
Positive sign indicates that the effect of both surface is convex.
Conclusion:
The focal length of a convex-concave lens is
(b)
The linear magnification of the image when the object is
Answer to Problem 38SP
Solution:
Explanation of Solution
Given data:
The object distance is
From the previous part, the focal length of a convex-concave lens is
Formula used:
Write the thin lens equation.
Here,
Write one expression for the magnification of an image.
Here,
Explanation:
Consider the thin lens equation.
Rearrange the above equation.
Substitute
Solve for
Write one expression for the magnification of an image.
Substitute
Negative sign indicates that the image is real and inverted.
Conclusion:
Therefore, the linear magnification of the image for the convex-concave lens is
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Chapter 38 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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