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Ch 34: Ray Optics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 34: Ray OpticsProblem 62
Chapter 34, Problem 62

BIO A dentist uses a curved mirror to view the back side of teeth in the upper jaw. Suppose she wants an upright image with a magnification of 1.5 when the mirror is 1.2 cm from a tooth. Should she use a convex or a concave mirror? What focal length should it have?

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Determine the type of mirror: Since the dentist wants an upright image, the mirror must produce a virtual image. Virtual images are formed by concave mirrors when the object is within the focal length. Therefore, the dentist should use a concave mirror.
Use the magnification formula to relate the image distance \( (d_i) \) and object distance \( (d_o) \): \( M = \frac{-d_i}{d_o} \). Here, \( M = 1.5 \) (positive because the image is upright) and \( d_o = 1.2 \ \text{cm} \). Rearrange the formula to solve for \( d_i \): \( d_i = -M \cdot d_o \).
Substitute the given values into the formula: \( d_i = -(1.5)(1.2) \). This will give the image distance \( d_i \), which is negative because the image is virtual.
Use the mirror equation to find the focal length \( f \): \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \). Substitute \( d_o = 1.2 \ \text{cm} \) and the calculated value of \( d_i \) into the equation.
Simplify the mirror equation to solve for \( f \): Rearrange the terms to isolate \( f \), and calculate its value. This will give the focal length of the concave mirror required to produce the desired image.

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Key Concepts

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

Mirror Types

Mirrors can be classified into two main types: concave and convex. A concave mirror curves inward and can produce real or virtual images depending on the object's position relative to the focal point. In contrast, a convex mirror curves outward and always produces virtual images that are smaller than the object. Understanding these properties is crucial for determining which type of mirror the dentist should use.
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Magnification

Magnification is the ratio of the height of the image to the height of the object. It indicates how much larger or smaller the image appears compared to the actual object. A magnification of 1.5 means the image is 1.5 times larger than the object. This concept is essential for the dentist to achieve the desired image size when using the mirror.
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Focal Length

The focal length of a mirror is the distance from the mirror's surface to its focal point, where parallel rays of light converge or appear to diverge. For concave mirrors, the focal length is positive, while for convex mirrors, it is negative. The focal length is critical in determining the characteristics of the image produced, including its size and orientation, which the dentist needs to consider for effective viewing.
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Textbook Question

A 25-cm-long rod lies along the optical axis of a converging lens, perpendicular to the lens plane. The lens has a 30 cm focal length. The rod's real , along the optical axis on the other side of the lens, is also 25 cm long. What is the distance from the lens to the nearest end of the rod?

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Textbook Question

There's one angle of incidence β onto a prism for which the light inside an isosceles prism travels parallel to the base and emerges at angle β. A laboratory measurement finds that β=52.2° for a prism shaped like an equilateral triangle. What is the prism's index of refraction?

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Textbook Question

You're visiting the shark tank at the aquarium when you see a 2.5-m-long shark that appears to be swimming straight toward you at 2.0 m/s. What is the shark's actual speed through the water? You can ignore the glass wall of the tank.

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Textbook Question

A 2.0-cm-tall candle flame is 2.0 m from a wall. You happen to have a lens with a focal length of 32 cm. How many places can you put the lens to form a well-focused image of the candle flame on the wall? For each location, what are the height and orientation of the image?

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Textbook Question

Paraxial light rays approach a transparent sphere parallel to an optical axis passing through the center of the sphere. The rays come to a focus on the far surface of the sphere. What is the sphere's index of refraction?

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Textbook Question

BIO A keratometer is an optical device used to measure the radius of curvature of the eye's cornea—its entrance surface. This measurement is especially important when fitting contact lenses, which must match the cornea's curvature. Most light incident on the eye is transmitted into the eye, but some light reflects from the cornea, which, due to its curvature, acts like a convex mirror. The keratometer places a small, illuminated ring of known diameter 7.5 cm in front of the eye. The optometrist, using an eyepiece, looks through the center of this ring and sees a small virtual image of the ring that appears to be behind the cornea. The optometrist uses a scale inside the eyepiece to measure the diameter of the image and calculate its magnification. Suppose the optometrist finds that the magnification for one patient is 0.049. What is the absolute value of the radius of curvature of her cornea?

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