Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 36, Problem 36.27P

You unconsciously estimate the distance to an object from the angle it subtends in your field of view. This angle θ in radians is related to the linear height of the object h and to the distance d by θ = h/d. Assume yon are driving a car and another car, 1.50 m high, is 24.0 m behind you. (a) Suppose your car has a flat passenger-side rearview mirror, 1.55 m from your eyes. How far from your eyes is the image of the car following you? (b) What angle does the image subtend in your field of view? (c) What If? Now suppose your car has a convex rearview mirror with a radius of curvature of magnitude 2.00 m (as suggested in Fig. 35.15). How far from your eyes is the image of the car behind you? (d) What angle does the image subtend at your eyes? (e) Based on its angular size, how far away does the following car appear to be?

(a)

Expert Solution
Check Mark
To determine
The distance of the image of car that is following the person.

Answer to Problem 36.27P

The image of the car is at 25.6m form the observer’s eye.

Explanation of Solution

Given info: The height of the following car is 1.50m . The distance between the observer’s eyes and the flat rear view mirror is 1.55m and the distance between the cars is 24.0m

The rear view mirror is flat plane mirror and for the case of plane mirror the object distance is same as the image distance. Therefore the image distance for the following car is same as the car itself.

Hence, the distance of the car from observer eyes as seen through the flat rear view side mirror is,

dec=dom+dimage (1)

Here,

dec is the distance of the image of the car from observers eye.

dom is the distance between the observer’s eye and the rear view mirror.

dimage is the distance of the image from the mirror.

Substitute 1.55m for dom and dimage in equation (1),

dec=dom+dimage=1.55m+24m=25.6m

Conclusion:

Therefore, the image of the car form the observer’s eye is at distance of 25.6m .

(b)

Expert Solution
Check Mark
To determine
The angle subtended by the image for the observer.

Answer to Problem 36.27P

The angle subtended is 0.0587radian .

Explanation of Solution

Given info: The height of the following car is 1.50m . The distance between the observer’s eyes and the flat rear view mirror is 1.55m and the distance between the cars is 24.0m .

Formula to calculate the angle subtended by the object,

θ=hd (2)

Here,

θ is the angle subtended.

h is the height of the object.

d is the distance of the object from the eye.

For the case of plane mirrors the object height and image height are equal and object distance and image distance are equal. Hence, to find the angle subtended by the image of the following car

Substitute 1.50m for h and 25.55m for d in the equation (2).

θ=hdθ=1.50m25.50m=0.0587radians

Conclusion:

Therefore, the angle subtended is 0.0587radians .

(c)

Expert Solution
Check Mark
To determine
The image distance from the observers eye if the rear view mirror is a convex mirror.

Answer to Problem 36.27P

The image is at 2.51m from the observer’s eyes.

Explanation of Solution

Given info: The height of the following car is 1.50m . The distance between the observer’s eyes and the convex rear view mirror is 1.55m and the distance between the cars is 24.0m . The radius of curvature of the mirror is 2.00m .

Formula to calculate the image distance form a convex mirror for a given object is

1p+1q=2R (3)

Here,

p is the object distance.

q is the image distance.

R is the radius of the curvature.

Substitute 24m for p , 2m for R in equation (1),

Negative R because it is a convex lens.

1p+1q=2R124m+1q=22q=0.96m (4)

The image distance is negative because the image is formed behind the mirror. Therefore the image distance from the observer’s eye is,

d=dom+q (5)

Here,

d is the required distance between the observers eye and the image.

dom is the distance between the observer’s eye and the convex rear view mirror.

Substitute 0.96m for q and 1.55m for dom in equation (5),

d=dom+qd=1.55m+0.960md=2.51m (6)

Conclusion:

Therefore, the image of the following car is at 2.51m form the observer’s eye in case of the convex rear view mirror.

(d)

Expert Solution
Check Mark
To determine
The angle subtended in the image of view for the observer in the case of convex rear view mirror.

Answer to Problem 36.27P

The angle subtended is 0.0239radian .

Explanation of Solution

Given info: The height of the following car is 1.50m . The distance between the observer’s eyes and the flat rear view mirror is 1.55m and the distance between the cars is 24.0m . The radius of curvature of the mirror is 2.00m .

From Equation (2) formula to calculate the angle subtended by the image,

θ=hd (7)

Here,

θ is the angle subtended.

h is the height of the image.

d is the distance of the image from the observer’s eye.

For the case of convex mirrors the object height and image height are not equal.

Formula to calculate the image height is,

hh=qp (8)

Here,

h is the height of object

Substitute 0.96m for q form equation (4) 1.50m for h and 24.0m for p in equation (6),

hh=qph24m=(0.96m24m)h=+0.060m (9)

From equation (6) and equation (9) respectively, substitute +0.060m for h and 2.51m for d in equation (8),

θ=hd=0.060m2.51m=0.0239radians . (10)

Conclusion:

Therefore, the angle subtended is 0.0239radians .

(e)

Expert Solution
Check Mark
To determine
The distance of the following car based on the angle subtended by the image in the observers eye.

Answer to Problem 36.27P

The distance of the following car based on the angular spread in the human eye is 62.8m .

Explanation of Solution

Given info: The height of the following car is 1.50m . The distance between the observer’s eyes and the flat rear view mirror is 1.55m and the distance between the cars is 24.0m . The radius of curvature of the mirror is 2.00m .

Formula to calculate the angle subtended by the image,

θ=hd (11)

Here,

θ is the angle subtended by the image as seen by the observer in the mirror.

h is the height of the car.

d is the distance of the car that appears to the observer’s eye.

Substitute 0.0239radians for θ form equation (10) 1.50m for h in equation (11),

θ=hd0.0239radians=1.50mdd=62.8m

Conclusion:

Therefore, the image appears to be 62.8m when viewed from the convex mirror.

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Chapter 36 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 36 - An object is located 50.0 cm from a converging...Ch. 36 - Prob. 36.4OQCh. 36 - A converging lens in a vertical plane receives...Ch. 36 - Prob. 36.6OQCh. 36 - Prob. 36.7OQCh. 36 - Prob. 36.8OQCh. 36 - A person spearfishing from a boat sees a...Ch. 36 - Prob. 36.10OQCh. 36 - A converging lens made of crown glass has a focal...Ch. 36 - A converging lens of focal length 8 cm forms a...Ch. 36 - Prob. 36.13OQCh. 36 - An object, represented by a gray arrow, is placed...Ch. 36 - Prob. 36.1CQCh. 36 - Prob. 36.2CQCh. 36 - Why do some emergency vehicles have the symbol...Ch. 36 - Prob. 36.4CQCh. 36 - Prob. 36.5CQCh. 36 - Explain why a fish in a spherical goldfish bowl...Ch. 36 - Prob. 36.7CQCh. 36 - Lenses used in eyeglasses, whether converging or...Ch. 36 - Suppose you want to use a converging lens to...Ch. 36 - Consider a spherical concave mirror with the...Ch. 36 - In Figures CQ36.11a and CQ36.11b, which glasses...Ch. 36 - Prob. 36.12CQCh. 36 - Prob. 36.13CQCh. 36 - Prob. 36.14CQCh. 36 - Prob. 36.15CQCh. 36 - Prob. 36.16CQCh. 36 - Prob. 36.17CQCh. 36 - Determine the minimum height of a vertical flat...Ch. 36 - In a choir practice room, two parallel walls are...Ch. 36 - (a) Does your bathroom mirror show you older or...Ch. 36 - Prob. 36.4PCh. 36 - A periscope (Fig. P35.3) is useful for viewing...Ch. 36 - Two flat mirrors have their reflecting surfaces...Ch. 36 - Two plane mirrors stand facing each other, 3.00 m...Ch. 36 - An object is placed 50.0 cm from a concave...Ch. 36 - A concave spherical mirror has a radius of...Ch. 36 - An object is placed 20.0 cm from a concave...Ch. 36 - A convex spherical mirror has a radius of...Ch. 36 - Prob. 36.12PCh. 36 - An object of height 2.00 cm is placed 30.0 cm from...Ch. 36 - A dentist uses a spherical mirror to examine a...Ch. 36 - A large hall in a museum has a niche in one wall....Ch. 36 - Why is the following situation impossible? At a...Ch. 36 - Prob. 36.17PCh. 36 - A certain Christmas tree ornament is a silver...Ch. 36 - (a) A concave spherical mirror forms an inverted...Ch. 36 - (a) A concave spherical mirror forms ail inverted...Ch. 36 - An object 10.0 cm tall is placed at the zero mark...Ch. 36 - A concave spherical mirror has a radius of...Ch. 36 - A dedicated sports car enthusiast polishes the...Ch. 36 - A convex spherical mirror has a focal length of...Ch. 36 - A spherical mirror is to be used to form an image...Ch. 36 - Review. A ball is dropped at t = 0 from rest 3.00...Ch. 36 - You unconsciously estimate the distance to an...Ch. 36 - Prob. 36.28PCh. 36 - One end of a long glass rod (n = 1.50) is formed...Ch. 36 - A cubical block of ice 50.0 cm on a side is placed...Ch. 36 - Prob. 36.31PCh. 36 - Prob. 36.32PCh. 36 - A flint glass, plate rests on the bottom of an...Ch. 36 - Figure P35.20 (page 958) shows a curved surface...Ch. 36 - Prob. 36.35PCh. 36 - Prob. 36.36PCh. 36 - A goldfish is swimming at 2.00 cm/s toward the...Ch. 36 - A thin lens has a focal length of 25.0 cm. Locate...Ch. 36 - An object located 32.0 cm in front of a lens forms...Ch. 36 - An object is located 20.0 cm to the left of a...Ch. 36 - The projection lens in a certain slide projector...Ch. 36 - An objects distance from a converging lens is 5.00...Ch. 36 - A contact lens is made of plastic with an index of...Ch. 36 - A converging lens has a focal length of 10.0 cm....Ch. 36 - A converging lens has a focal length of 10.0 cm....Ch. 36 - A diverging lens has a focal length of magnitude...Ch. 36 - Prob. 36.47PCh. 36 - Suppose an object has thickness dp so that it...Ch. 36 - The left face of a biconvex lens has a radius of...Ch. 36 - In Figure P35.30, a thin converging lens of focal...Ch. 36 - An antelope is at a distance of 20.0 m from a...Ch. 36 - Prob. 36.52PCh. 36 - A 1.00-cm-high object is placed 4.00 cm to the...Ch. 36 - The magnitudes of the radii of curvature are 32.5...Ch. 36 - Two rays traveling parallel to the principal axis...Ch. 36 - Prob. 36.56PCh. 36 - Figure 35.34 diagrams a cross section of a camera....Ch. 36 - Josh cannot see objects clearly beyond 25.0 cm...Ch. 36 - Prob. 36.59PCh. 36 - A person sees clearly wearing eyeglasses that have...Ch. 36 - Prob. 36.61PCh. 36 - A certain childs near point is 10.0 cm; her far...Ch. 36 - A person is to be fitted with bifocals. She can...Ch. 36 - A simple model of the human eye ignores its lens...Ch. 36 - A patient has a near point of 45.0 cm and far...Ch. 36 - A lens that has a focal length of 5.00 cm is used...Ch. 36 - The distance between the eyepiece and the...Ch. 36 - The refracting telescope at the Yerkes Observatory...Ch. 36 - A certain telescope has an objective mirror with...Ch. 36 - Astronomers often take photographs with the...Ch. 36 - Prob. 36.71APCh. 36 - A real object is located at the zero end of a...Ch. 36 - The distance between an object and its upright...Ch. 36 - Prob. 36.74APCh. 36 - Andy decides to use an old pair of eyeglasses to...Ch. 36 - Prob. 36.76APCh. 36 - The lens and mirror in Figure P36.77 are separated...Ch. 36 - Two converging lenses having focal lengths of f1 =...Ch. 36 - Figure P36.79 shows a piece of glass with index of...Ch. 36 - Prob. 36.80APCh. 36 - The object in Figure P36.81 is midway between the...Ch. 36 - In many applications, it is necessary to expand or...Ch. 36 - Prob. 36.83APCh. 36 - Prob. 36.84APCh. 36 - Two lenses made of kinds of glass having different...Ch. 36 - Why is the following situation impossible?...Ch. 36 - An object is placed 12.0 cm to the left of a...Ch. 36 - An object is placed a distance p to the left of a...Ch. 36 - An observer to the right of the mirror-lens...Ch. 36 - In a darkened room, a burning candle is placed...Ch. 36 - Prob. 36.91APCh. 36 - An object 2.00 cm high is placed 40.0 cm to the...Ch. 36 - Assume the intensity of sunlight is 1.00 kW/m2 at...Ch. 36 - A zoom lens system is a combination of lenses that...Ch. 36 - Figure P36.95 shows a thin converging lens for...Ch. 36 - A floating strawberry illusion is achieved with...Ch. 36 - Consider the lensmirror arrangement shown in...
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