Skip to main content
Ch 35: Optical Instruments
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 35: Optical InstrumentsProblem 34
Chapter 35, Problem 34

The cornea, a boundary between the air and the aqueous humor, has a 3.0 cm focal length when acting alone. What is its radius of curvature?

Verified step by step guidance
1
Step 1: Understand the relationship between the focal length and the radius of curvature for a lens or curved surface. The formula to use is the Lensmaker's equation for a single refractive surface: \( R = 2f \), where \( R \) is the radius of curvature and \( f \) is the focal length.
Step 2: Identify the given values in the problem. The focal length \( f \) is provided as 3.0 cm.
Step 3: Substitute the given focal length into the formula \( R = 2f \). This means \( R = 2 \times 3.0 \, \text{cm} \).
Step 4: Perform the multiplication to find the radius of curvature. This step involves calculating \( R \) using the formula.
Step 5: Interpret the result. The radius of curvature \( R \) represents the distance from the center of the cornea's curvature to its surface, and it is directly proportional to the focal length.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

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

Focal Length

The focal length of a lens or mirror is the distance from the lens or mirror to the focal point, where parallel rays of light converge. In optics, the focal length is crucial for determining how a lens will bend light and is inversely related to the curvature of the lens. A shorter focal length indicates a more powerful lens that can bend light more sharply.
Recommended video:
Guided course
10:54
Spinning on a string of variable length

Radius of Curvature

The radius of curvature is the radius of the sphere from which a lens or mirror segment is taken. It is a measure of how 'curved' the surface is; a smaller radius indicates a steeper curve. In the context of lenses, the radius of curvature is directly related to the focal length, as described by the lens maker's equation.
Recommended video:
Guided course
06:18
Calculating Radius of Nitrogen

Lens Maker's Equation

The lens maker's equation relates the focal length of a lens to the radii of curvature of its two surfaces and the refractive index of the material. It is expressed as 1/f = (n - 1) * (1/R1 - 1/R2), where f is the focal length, n is the refractive index, and R1 and R2 are the radii of curvature of the lens surfaces. This equation is essential for calculating the radius of curvature when the focal length and refractive index are known.
Recommended video:
05:38
Lens Maker Equation
Related Practice
Textbook Question

A microscope with a tube length of 180 mm achieves a total magnification of 800x with a 40x objective and a 20x eyepiece. The microscope is focused for viewing with a relaxed eye. Approximately how far is the sample from the objective lens?

1
views
Textbook Question

Mars (6800 km diameter) is viewed through a telescope on a night when it is 1.1 x 10⁸ km from the earth. Its angular size as seen through the eyepiece is 0.50°, the same size as the full moon seen by the naked eye. If the eyepiece focal length is 25 mm, how long is the telescope?

1
views
Textbook Question

A 1.0-cm-tall object is 110 cm from a screen. A diverging lens with focal length -20 cm is 20 cm in front of the object. What are the focal length and distance from the screen of a second lens that will produce a well-focused, 2.0-cm-tall on the screen?

1
views
Textbook Question

Marooned on a desert island and with a lot of time on your hands, you decide to disassemble your glasses to make a crude telescope with which you can scan the horizon for rescuers. Luckily you’re farsighted, and, like most people, your two eyes have different lens prescriptions. Your left eye uses a lens of power +4.5 D, and your right eye’s lens is +3.0 D. Which lens should you use for the objective and which for the eyepiece? Explain.

3
views
Textbook Question

A 15-cm-focal-length converging lens is 20 cm to the right of a 7.0-cm-focal-length converging lens. A 1.0-cm-tall object is distance L to the left of the 7.0-cm-focal-length lens. What are the height and orientation of the final image?

2
views
Textbook Question

A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P35.28. The parallel rays of a laser beam of width w₁ enter from the left. What is the width w2 of the exiting laser beam?

1
views