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physics
college physics 2nd
College Physics 2nd Edition OpenStax - Solutions
A very myopic man has a far point of 20.0 cm. What power contact lens (when on the eye) will correct his distant vision?
Why not have the objective of a microscope form a case 2 image with a large magnification?
Repeat the previous problem for eyeglasses held 1.50 cm from the eyes.Previous ProblemA very myopic man has a far point of 20.0 cm. What power contact lens (when on the eye) will correct his distant vision?
What advantages do oil immersion objectives offer?
How does the NA of a microscope compare with the NA of an optical fiber?
Repeat the previous problem for glasses that are 1.75 cm from the eyes.Previous ProblemA myopic person sees that their contact lens prescription is -4.00 D. What is their far point?
If you want your microscope or telescope to project a real image onto a screen, how would you change the placement of the eyepiece relative to the objective?
The contact lens prescription for a mildly farsighted person is 0.750 D, and the person has a near point of 29.0 cm. What is the power of the tear layer between the cornea and the lens if the correction is ideal, taking the tear layer into account?
List the various types of aberrations. What causes them and how can each be reduced?
A nearsighted man cannot see objects clearly beyond 20 cm from his eyes. How close must he stand to a mirror in order to see what he is doing when he shaves?
A teacher sees that a child’s contact lens prescription is 0.750 D. What is the child’s near point?
Repeat the previous problem for glasses that are 2.20 cm from the eyes.Previous ProblemA teacher sees that a child’s contact lens prescription is 0.750 D. What is the child’s near point?
The contact lens prescription for a nearsighted person is -4.00 D and the person has a far point of 22.5 cm. What is the power of the tear layer between the cornea and the lens if the correction is ideal, taking the tear layer into account?
A boy has a near point of 50 cm and a far point of 500 cm. Will a -4.00 D lens correct his far point to infinity?
A microscope with an overall magnification of 800 has an objective that magnifies by 200.(a) What is the magnification of the eyepiece? (b) If there are two other objectives that can be used, having magnifications of 100 and 400, what other total magnifications are possible?
(a) What magnification is produced by a 0.150 cm focal length microscope objective that is 0.155 cm from the object being viewed? (b) What is the overall magnification if an 8 × eyepiece (one that produces a magnification of 8.00) is used?
(a) Where does an object need to be placed relative to a microscope for its 0.500 cm focal length objective to produce a magnification of -400? (b) Where should the 5.00 cm focal length eyepiece be placed to produce a further fourfold (4.00) magnification?
You switch from a 1.40 NA 60 × oil immersion objective to a 1.40 NA 60 × oil immersion objective. What are the acceptance angles for each? Compare and comment on the values. Which would you use first to locate the target area on your specimen?
An amoeba is 0.305 cm away from the 0.300 cm focal length objective lens of a microscope.(a) Where is the image formed by the objective lens?(b) What is this image’s magnification? (c) An eyepiece with a 2.00 cm focal length is placed 20.0 cm from the objective. Where is the final image? (d)
What is the angular magnification of a telescope that has a 100 cm focal length objective and a 2.50cm focal length eyepiece?
Find the distance between the objective and eyepiece lenses in the telescope in the above problem needed to produce a final image very far from the observer, where vision is most relaxed. Note that a telescope is normally used to view very distant objects.
A large reflecting telescope has an objective mirror with a 10.0m radius of curvature. What angular magnification does it produce when a 3.00 cm focal length eyepiece is used?
A small telescope has a concave mirror with a 2.00 m radius of curvature for its objective. Its eyepiece is a 4.00 cm focal length lens.(a) What is the telescope’s angular magnification? (b) What angle is subtended by a 25,000 km diameter sunspot? (c) What is the angle of its telescopic image?
Consider a telescope of the type used by Galileo, having a convex objective and a concave eyepiece as illustrated in Figure 26.23(a). Construct a problem in which you calculate the location and size of the image produced. Among the things to be considered are the focal lengths of the lenses and
Critical Thinking A microscope has the objective lens 6.00 mm from an object. The focal length of the objective lens is 4.00 mm. The eyepiece has a focal length of 50.0 mm and is initially 25.0 mm from the objective lens.(a) The objective lens is moved to 5.00 mm from the objective, effectively
Calculate the speed of light in zircon, a material used in jewelry to imitate diamond.StrategyThe speed of light in a material, v, can be calculated from the index of refraction of the material using the equation n = c/v.
Find the index of refraction for medium 2 in Figure 25.12(a), assuming medium 1 is air and given the incident angle is 30.0 and the angle of refraction is 22.0°.StrategyThe index of refraction for air is taken to be 1 in most cases (and up to four significant figures, it is 1.000). Thus n = 1.00
Show that when light reflects from two mirrors that meet each other at a right angle, the outgoing ray is parallel to the incoming ray, as illustrated in the following figure. 0₁ 0202 0₁
Suppose that in a situation like that in Example 25.2, light goes from air to diamond and that the incident angle is 30.0°. Calculate the angle of refraction θ2 in the diamond.StrategyAgain the index of refraction for air is taken to be n1 = 1.00, and we are given θ1 = 30.0. We can look up the
Light shows staged with lasers use moving mirrors to swing beams and create colorful effects. Show that a light ray reflected from a mirror changes direction by 2θ when the mirror is rotated by an angle θ.
What is the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air?StrategyThe index of refraction for polystyrene is found to be 1.49 in Figure 25.14, and the index of refraction of air can be taken to be 1.00, as before. Thus, the condition that the second
A flat mirror is neither converging nor diverging. To prove this, consider two rays originating from the same point and diverging at an angle θ. Show that after striking a plane mirror, the angle between their directions remains θ. да оздо Өг
Suppose you take a magnifying glass out on a sunny day and you find that it concentrates sunlight to a small spot 8.00 cm away from the lens. What are the focal length and power of the lens?StrategyThe situation here is the same as those shown in Figure 25.25 and Figure 25.26. The Sun is so far
What is the speed of light in water? In glycerine?
A clear glass light bulb is placed 0.750 m from a convex lens having a 0.500 m focal length, as shown in Figure 25.33. Use ray tracing to get an approximate location for the image. Then use the thin lens equations to calculate(a) The location of the image and(b) Its magnification. Verify that ray
What is the speed of light in air? In crown glass?
Calculate the index of refraction for a medium in which the speed of light is 2.012 x 108 m/s, and identify the most likely substance based on Table 25.1.Data from Table 25.1 Medium Gases at 0°C, 1 atm Air Carbon dioxide Hydrogen Oxygen Liquids at 20°C Benzene Carbon disulfide Carbon
Suppose the book page in Figure 25.35 (a) is held 7.50 cm from a convex lens of focal length 10.0 cm, such as a typical magnifying glass might have. What magnification is produced?Strategy and ConceptWe are given that do = 7.50 cm and f = 10.0 cm, so we have a situation where the object is placed
In what substance in Table 25.1 is the speed of light 2.290 x 108 m/s?Data from Table 25.1 Medium Gases at 0°C, 1 atm Air Carbon dioxide Hydrogen Oxygen Liquids at 20°C Benzene Carbon disulfide Carbon tetrachloride Ethanol Glycerine Water, fresh Solids at
Suppose an object such as a book page is held 7.50 cm from a concave lens of focal length –10.0 cm. Such a lens could be used in eyeglasses to correct pronounced nearsightedness. What magnification is produced?Strategy and ConceptThis example is identical to the preceding one, except that the
Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR follows the same law of reflection as visible light. Given that the mirror has a radius of curvature of 50.0 cm and produces an image of the coils 3.00 m away from the mirror, where are the
There was a major collision of an asteroid with the Moon in medieval times. It was described by monks at Canterbury Cathedral in England as a red glow on and around the Moon. How long after the asteroid hit the Moon, which is 3.84 x 105 km away, would the light first arrive on Earth?
One of the solar technologies used today for generating electricity is a device (called a parabolic trough or concentrating collector) that concentrates the sunlight onto a blackened pipe that contains a fluid. This heated fluid is pumped to a heat exchanger, where its heat energy is transferred to
A scuba diver training in a pool looks at his instructor as shown in Figure 25.51. What angle does the ray from the instructor's face make with the perpendicular to the water at the point where the ray enters? The angle between the ray in the water and the perpendicular to the water is 25.0°. 2.0
A keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image. The smaller the magnification, the smaller the radius of
Components of some computers communicate with each other through optical fibers having an index of refraction n = 1.55. What time in nanoseconds is required for a signal to travel 0.200 m through such a fiber?
(a) Given that the angle between the ray in the water and the perpendicular to the water is 25.0°, and using information in Figure 25.51, find the height of the instructor's head above the water, noting that you will first have to calculate the angle of refraction. (b) Find the apparent depth of
On the Moon's surface, lunar astronauts placed a corner reflector, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. What percent correction is needed to account for the delay in time due to the slowing of light in Earth's atmosphere?
Suppose Figure 25.52 represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass (Δx), given that the incident angle is 40.0° and the glass is 1.00 cm thick. n чи N3 20 0₂ Өз 03 |--xv--|
Figure 25.52 shows a ray of light passing from one medium into a second and then a third. Show that θ3 is the same as it would be if the second medium were not present (provided total internal reflection does not occur). n₁ M2 N3 02 өг Өз Өз |--Ax--|
Suppose light travels from water to another substance, with an angle of incidence of 10.0° and an angle of refraction of 14.9°. (a) What is the index of refraction of the other substance? (b) What is unreasonable about this result?(c) Which assumptions are unreasonable or inconsistent?
Light traveling from water to a gemstone strikes the surface at an angle of 80.0° and has an angle of refraction of 15.2°.(a) What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
Verify that the critical angle for light going from water to air is 48.6°, as discussed at the end of Example 25.4, regarding the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air.Data from Example 25.4What is the critical angle for light traveling in a
(a) At the end of Example 25.4, it was stated that the critical angle for light going from diamond to air is 24.4°. Verify this. (b) What is the critical angle for light going from zircon to air?Data From Example 25.4What is the critical angle for light traveling in a polystyrene (a type of
An optical fiber uses flint glass clad with crown glass. What is the critical angle?
At what minimum angle will you get total internal reflection of light traveling in water and reflected from ice?
Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is 45.0°, what must be the minimum index of refraction of the material from which the reflector is made?
You can determine the index of refraction of a substance by determining its critical angle.(a) What is the index of refraction of a substance that has a critical angle of 68.4° when submerged in water? What is the substance, based on Table 25.1? (b) What would the critical angle be for this
A ray of light, emitted beneath the surface of an unknown liquid with air above it, undergoes total internal reflection as shown in Figure 25.53. What is the index of refraction for the liquid and its likely identification? 7₂ n₁ To 0 - 13.4 cm. 15.0 cm
A light ray entering an optical fiber surrounded by air is first refracted and then reflected as shown in Figure 25.54. Show that if the fiber is made from crown glass, any incident ray will be totally internally reflected. n₁n₂ 01. 02 03:
(a) What is the ratio of the speed of red light to violet light in diamond, based on Table 25.2? (b) What is this ratio in polystyrene?(c) Which is more dispersive?Data From Table 25.2 Medium Water Diamond Glass, crown Red (660 nm) 1.331 2.410 1.512 Glass, flint 1.662 Polystyrene
A beam of white light goes from air into water at an incident angle of 75.0°. At what angles are the red (660 nm) and violet (410 nm) parts of the light refracted?
By how much do the critical angles for red (660 nm) and violet (410 nm) light differ in a diamond surrounded by air?
(a) A narrow beam of light containing yellow (580 nm) and green (550 nm) wavelengths goes from polystyrene to air, striking the surface at a 30.0° incident angle. What is the angle between the colors when they emerge? (b) How far would they have to travel to be separated by 1.00 mm?
A parallel beam of light containing orange (610 nm) and violet (410 nm) wavelengths goes from fused quartz to water, striking the surface between them at a 60.0° incident angle. What is the angle between the two colors in water?
A narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air through a 1.00 cm thick flat piece of crown glass and back to air again. The beam strikes at a 30.0° incident angle. (a) At what angles do the two colors emerge? (b) By what distance are the red and
A narrow beam of white light enters a prism made of crown glass at a 45.0° incident angle, as shown in Figure 25.55. At what angles, θR and θV, do the red (660 nm) and violet (410 nm) components of the light emerge from the prism? Incident light 45°C 60° 60° Red (660 nm) 60° Violet (410 nm)
What is the power in diopters of a camera lens that has a 50.0 mm focal length?
What is the focal length of 1.75 D reading glasses found on the rack in a pharmacy?
You note that your prescription for new eyeglasses is –4.50 D. What will their focal length be?
How far from the lens must the film in a camera be, if the lens has a 35.0 mm focal length and is being used to photograph a flower 75.0 cm away? Explicitly show how you follow the steps in the Problem-Solving Strategy for lenses.
A certain slide projector has a 100 mm focal length lens. (a) How far away is the screen, if a slide is placed 103 mm from the lens and produces a sharp image?(b) If the slide is 24.0 by 36.0 mm, what are the dimensions of the image? Explicitly show how you follow the steps in the Problem-Solving
A doctor examines a mole with a 15.0 cm focal length magnifying glass held 13.5 cm from the mole (a) Where is the image?(b) What is its magnification? (c) How big is the image of a 5.00 mm diameter mole?
A camera with a 50.0 mm focal length lens is being used to photograph a person standing 3.00 m away. (a) How far from the lens must the film be?(b) If the film is 36.0 mm high, what fraction of a 1.75 m tall person will fit on it? (c) Discuss how reasonable this seems, based on your experience in
A camera lens used for taking close-up photographs has a focal length of 22.0 mm. The farthest it can be placed from the film is 33.0 mm.(a) What is the closest object that can be photographed? (b) What is the magnification of this closest object?
Suppose your 50.0 mm focal length camera lens is 51.0 mm away from the film in the camera. (a) How far away is an object that is in focus? (b) What is the height of the object if its image is 2.00 cm high?
(a) What is the focal length of a magnifying glass that produces a magnification of 3.00 when held 5.00 cm from an object, such as a rare coin? (b) Calculate the power of the magnifier in diopters.(c) Discuss how this power compares to those for store-bought reading glasses (typically 1.0 to 4.0
Suppose a 200 mm focal length telephoto lens is being used to photograph mountains 10.0 km away. (a) Where is the image? (b) What is the height of the image of a 1000 m high cliff on one of the mountains?
A camera with a 100 mm focal length lens is used to photograph the sun and moon. What is the height of the image of the sun on the film, given the sun is 1.40 x 106 km in diameter and is 1.50 x 108 km away?
Combine thin lens equations to show that the magnification for a thin lens is determined by its focal length and the object distance and is given by m = f/(f - do).
What is the focal length of a makeup mirror that has a power of 1.50 D?
Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace a 800 mm focal length telephoto lens?
(a) Calculate the focal length of the mirror formed by the shiny back of a spoon that has a 3.00 cm radius of curvature. (b) What is its power in diopters?
Find the magnification of the heater element in Example 25.9. Note that its large magnitude helps spread out the reflected energy.Data from Example 25.9Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR follows the same law of reflection as
A shopper standing 3.00 m from a convex security mirror sees his image with a magnification of 0.250. (a) Where is his image?(b) What is the focal length of the mirror? (c) What is its radius of curvature? Explicitly show how you follow the steps in the Problem-Solving Strategy for Mirrors.
An object 1.50 cm high is held 3.00 cm from a person’s cornea, and its reflected image is measured to be 0.167 cm high. (a) What is the magnification? (b) Where is the image? (c) Find the radius of curvature of the convex mirror formed by the cornea. (Note that this technique is used by
Ray tracing for a flat mirror shows that the image is located a distance behind the mirror equal to the distance of the object from the mirror. This is stated di = -do, since this is a negative image distance (it is a virtual image). (a) What is the focal length of a flat mirror?(b) What is its
Show that for a flat mirror hi = ho, knowing that the image is a distance behind the mirror equal in magnitude to the distance of the object from the mirror.
Use the law of reflection to prove that the focal length of a mirror is half its radius of curvature. That is, prove that f= R/2. Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature. The Law of Reflection The angle of reflection equals the
Calculate the intensity of IR radiation in W/m2 projected by the concave mirror on a person 3.00 m away. Assume that the heating element radiates 1500 W and has an area of 100 cm2, and that half of the radiated power is reflected and focused by the mirror.
Consider a 250-W heat lamp fixed to the ceiling in a bathroom. If the filament in one light burns out then the remaining three still work. Construct a problem in which you determine the resistance of each filament in order to obtain a certain intensity projected on the bathroom floor. The ceiling
Light composed of multiple frequencies passes through crown glass.(a) How much faster does the violet component of the light with a wavelength of 410 nm travel in the crown glass than the component of orange light with a wavelength of 610 nm?(b) In a mechanical situation with friction, the longer
Calculate:(a) The number of moles in 1.00 m3 of gas at STP, and (b) The number of liters of gas per mole.
Assume the helium-neon lasers commonly used in student physics laboratories have power outputs of 0.250 mW.(a) If such a laser beam is projected onto a circular spot 1.00 mm in diameter, what is its intensity? (b) Find the peak magnetic field strength. (c) Find the peak electric field strength.
Distances in space are often quoted in units of light years, the distance light travels in one year.(a) How many meters is a light year? (b) How many meters is it to Andromeda, the nearest large galaxy, given that it is 2.00 × 106 light years away? (c) The most distant galaxy yet discovered is
Suppose your 60.0-L (15.9-gal) steel gasoline tank is full of gas, so both the tank and the gasoline have a temperature of 15.0°C. How much gasoline has spilled by the time they warm to 35.0°C?StrategyThe tank and gasoline increase in volume, but the gasoline increases more, so the amount spilled
What magnification will be produced by a lens of power –4.00 D (such as might be used to correct myopia) if an object is held 25.0 cm away?
(a) Find the magnetic field strength when the electric field strength is 1,250 V/m. (b) If E is increased, would B be increased, decreased, or remain the same? (c) By what factor would the change in part b be, if any?
If the Sun suddenly turned off, we would not know it until its light stopped coming. How long would that be, given that the Sun is 1.50 × 1011 m away?
If you wish to detect details of the size of atoms (about 1x10-10 m) with electromagnetic radiation, it must have a wavelength of about this size. (a) What is its frequency? (b) What type of electromagnetic radiation might this be?
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