Skip to main content
Ch 34: Geometric Optics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 34: Geometric OpticsProblem 13b
Chapter 33, 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?

Verified step by step guidance
1
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

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.
Recommended video:
09:03
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.
Recommended video:
09:03
Mirror Equation

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.
Recommended video:
Guided course
06:18
Calculating Radius of Nitrogen
Related Practice
Textbook Question

A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 7.00 m from her. What is the depth of the water at this point?

3
views
Textbook Question

You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. Where is the of your 5.0-cm tall nose located?

1
views
Textbook Question

An object is 18.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.00 cm in diameter. What are the position and magnification of its ?

1
views
Textbook Question

The thin glass shell shown in Fig. E34.15 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm from the center of the mirror along the optic axis, as shown in the figure. Calculate the location and height of the of this seed.

1
views
Textbook Question

A Spherical Fish Bowl. A small tropical fish is at the center of a water-filled, spherical fish bowl 28.0 cm in diameter. Find the apparent position and magnification of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored.

3
views
Textbook Question

A spherical, concave shaving mirror has a radius of curvature of 32.0 cm. Where is the image? Is the image real or virtual?

1
views