Ch 34: Geometric Optics

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 34: Geometric Optics

Problem 49a

Chapter 34, Problem 49a

A camera lens has a focal length of 180.0 mm and an aperture diameter of 16.36 mm. What is the ƒ-number of the lens?

Verified step by step guidance

Step 1: Understand the concept of the ƒ-number. The ƒ-number (or focal ratio) is a dimensionless quantity that describes the light-gathering ability of a lens. It is defined as the ratio of the focal length (f) to the aperture diameter (D). The formula is ƒ-number = f / D.

Step 2: Identify the given values from the problem. The focal length of the lens is f = 180.0 mm, and the aperture diameter is D = 16.36 mm.

Step 3: Substitute the given values into the formula for the ƒ-number. Using MathML, the formula can be expressed as:

\frac{f}{D}

. Replace f with 180.0 mm and D with 16.36 mm.

Step 4: Perform the division to calculate the ƒ-number. Divide the focal length (180.0 mm) by the aperture diameter (16.36 mm). This will yield the ƒ-number.

Step 5: Interpret the result. The ƒ-number is a measure of how much light the lens can gather. A smaller ƒ-number indicates a larger aperture and more light-gathering ability, while a larger ƒ-number indicates a smaller aperture and less light-gathering ability.

Verified video answer for a similar problem:

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

Video duration:

Was this helpful?

Key Concepts

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

Focal Length

Focal length is the distance from the lens to the point where light rays converge to form a sharp image. It is a critical parameter that determines the lens's magnification and field of view. A longer focal length results in higher magnification, while a shorter focal length provides a wider field of view.

Aperture Diameter

The aperture diameter refers to the size of the opening in the lens through which light passes. It affects the amount of light entering the camera and influences the depth of field in an image. A larger aperture allows more light, resulting in a shallower depth of field, while a smaller aperture reduces light and increases depth of field.

ƒ-number (f-stop)

The ƒ-number, or f-stop, is a dimensionless number that represents the ratio of the lens's focal length to the diameter of the aperture. It indicates the lens's light-gathering ability; a lower ƒ-number means a larger aperture and more light, while a higher ƒ-number indicates a smaller aperture and less light. The ƒ-number is crucial for controlling exposure and depth of field in photography.

Recommended video:

Guided course

07:19

Moles & Avogadro's Number

Related Practice

Textbook Question

Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 45.0 cm from his eyes instead of the usual 25.0 cm. Is this person nearsighted or farsighted?

views

Textbook Question

Where is the near point of an eye for which a contact lens with a power of +2.75 diopters is prescribed?

views

Textbook Question

BIO The Lens of the Eye. The crystalline lens of the human eye is a double-convex lens made of material having an index of refraction of 1.44 (although this varies). Its focal length in air is about 8.0 mm, which also varies. We shall assume that the radii of curvature of its two surfaces have the same magnitude. Find the radii of curvature of this lens.

views

Textbook Question

Zoom Lens. Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f₁ = 12 cm, and the diverging lens has focal length f₂ = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. (a) For a distant object, where is the of the converging lens? (c) Where is the final image? Compare your answer to Fig. 34.43a.

views

Textbook Question

You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. If the dimensions of the picture on a 35 mm color slide are 24 mm ✖ 36 mm, what is the minimum size of the projector screen required to accommodate the image?

views

Textbook Question

BIO Ordinary Glasses. Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their power in diopters?

views