Textbook Question
What is the focal length of a second lens that could be placed in contact with the first lens to provide an overall power of 30 D?
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Ch 35: Optical Instruments
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 35, Problem 9
A camera takes a properly exposed photo at F5.6 and 1/125 s. What shutter speed should be used if the lens is changed to F4.0?
Verified step by step guidance1
Understand the relationship between aperture (f-stop) and exposure. The f-stop value determines the size of the aperture, which controls the amount of light entering the camera. Lower f-stop values (e.g., F4.0) allow more light, while higher f-stop values (e.g., F5.6) allow less light.
Recall the formula for exposure adjustment: the exposure is proportional to the square of the f-stop ratio. Specifically, the change in light is given by \( \left( \frac{f_1}{f_2} \right)^2 \), where \( f_1 \) is the original f-stop and \( f_2 \) is the new f-stop.
Calculate the ratio of the f-stops: \( \frac{5.6}{4.0} \). This ratio will help determine how much the exposure changes when switching from F5.6 to F4.0.
Determine the adjustment needed for the shutter speed. Since the aperture is letting in more light at F4.0, the shutter speed must be faster to maintain the same exposure. Use the inverse of the square of the f-stop ratio to calculate the new shutter speed.
Apply the calculated adjustment to the original shutter speed to find the new shutter speed. Ensure the new shutter speed is faster to compensate for the increased light entering the camera at F4.0.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exposure Triangle
The exposure triangle consists of three elements: aperture, shutter speed, and ISO. These elements work together to control the exposure of an image. Changing one element requires adjustments in the others to maintain the same exposure level. In this case, changing the aperture affects the amount of light entering the camera, necessitating a change in shutter speed to achieve proper exposure.
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Aperture
Aperture refers to the opening in a camera lens that controls the amount of light that reaches the sensor. It is measured in f-stops, with a lower f-stop number (like F4.0) allowing more light than a higher number (like F5.6). When the aperture is widened (lower f-stop), the camera needs a faster shutter speed to prevent overexposure, as more light is entering the camera.
Shutter Speed
Shutter speed is the duration for which the camera's shutter remains open to expose the sensor to light. It is typically measured in seconds or fractions of a second. A faster shutter speed allows less light to hit the sensor, which is necessary when the aperture is opened wider. In this scenario, adjusting the shutter speed is crucial to compensate for the increased light from changing the aperture from F5.6 to F4.0.
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Related Practice
Textbook Question
A camera’s close-up lens is aimed at a butterfly 200 mm in front of the lens, creating a focused on the detector 50 mm behind the lens. A proper exposure requires an f-number of F8.0. What is the correct diameter of the lens aperture?
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Textbook Question
What is the f-number of a relaxed eye with the pupil fully dilated to 8.0 mm? Model the eye as a single lens 2.4 cm in front of the retina.
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Textbook Question
What is the power of a lens with a focal length of 25 mm?
Textbook Question
Ramon has contact lenses with the prescription +2.0 D. What eye condition does Ramon have?
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Textbook Question
A magnifier has a magnification of 5x. How far from the lens should an object be held so that its is seen at the near-point distance of 25 cm? Assume that your eye is immediately behind the lens.
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