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Ch 34: Geometric Optics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 34: Geometric OpticsProblem 13b
Chapter 34, Problem 13b

Dental Mirror. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect with a magnification of 2.00 when the mirror is 1.25 cm from a tooth. (Treat this problem as though the object and lie along a straight line.) What must be the focal length and radius of curvature of this mirror?

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Start by understanding the relationship between magnification (M), object distance (d_o), and image distance (d_i). The magnification is given by the formula: M = -d_i / d_o. Since the magnification is positive and the image is erect, the mirror must be a concave mirror.
Given that the magnification (M) is 2.00 and the object distance (d_o) is 1.25 cm, use the magnification formula to find the image distance (d_i). Rearrange the formula to solve for d_i: d_i = -M * d_o.
Substitute the given values into the formula: d_i = -2.00 * 1.25 cm. Calculate d_i to find the image distance.
Use the mirror equation to find the focal length (f). The mirror equation is: 1/f = 1/d_o + 1/d_i. Substitute the values of d_o and d_i into this equation to solve for the focal length.
Once the focal length is determined, use the relationship between the focal length and the radius of curvature (R) for a mirror, which is: R = 2f. Calculate the radius of curvature using the focal length obtained from the previous step.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Magnification

Magnification is the process of enlarging the appearance of an object using optical instruments. It is defined as the ratio of the image height to the object height. In mirrors, magnification can also be expressed as the negative ratio of the image distance to the object distance. For an erect image with a magnification of 2.00, the image is twice the size of the object and is upright.
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Mirror Equation

Mirror Equation

The mirror equation relates the object distance (d_o), image distance (d_i), and the focal length (f) of a mirror: 1/f = 1/d_o + 1/d_i. This equation is crucial for determining the focal length when the object and image distances are known. It helps in understanding how the curvature of the mirror affects the formation of images.
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Radius of Curvature

The radius of curvature (R) of a mirror is the radius of the sphere from which the mirror segment is taken. It is related to the focal length by the equation R = 2f. This relationship is essential for determining the mirror's curvature, which affects how light is focused and how images are formed. A smaller radius indicates a more curved mirror, affecting the image properties.
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