Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 26, Problem 22P

(a)

To determine

The distance of the image of car that is following the person.

(a)

Expert Solution
Check Mark

Answer to Problem 22P

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)

To determine

The angle subtended by the image for the observer.

(b)

Expert Solution
Check Mark

Answer to Problem 22P

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)

To determine

The image distance from the observers eye if the rear view mirror is a convex mirror.

(c)

Expert Solution
Check Mark

Answer to Problem 22P

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)

To determine

The angle subtended in the image of view for the observer in the case of convex rear view mirror.

(d)

Expert Solution
Check Mark

Answer to Problem 22P

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)

To determine

The distance of the following car based on the angle subtended by the image in the observers eye.

(e)

Expert Solution
Check Mark

Answer to Problem 22P

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 26 Solutions

Principles of Physics: A Calculus-Based Text

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