Concept explainers
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)
Answer to Problem 36.27P
Explanation of Solution
Given info: The height of the following car is
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,
Here,
Substitute
Conclusion:
Therefore, the image of the car form the observer’s eye is at distance of
(b)
Answer to Problem 36.27P
Explanation of Solution
Given info: The height of the following car is
Formula to calculate the angle subtended by the object,
Here,
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
Conclusion:
Therefore, the angle subtended is
(c)
Answer to Problem 36.27P
Explanation of Solution
Given info: The height of the following car is
Formula to calculate the image distance form a convex mirror for a given object is
Here,
Substitute
Negative
The image distance is negative because the image is formed behind the mirror. Therefore the image distance from the observer’s eye is,
Here,
Substitute
Conclusion:
Therefore, the image of the following car is at
(d)
Answer to Problem 36.27P
Explanation of Solution
Given info: The height of the following car is
From Equation (2) formula to calculate the angle subtended by the image,
Here,
For the case of convex mirrors the object height and image height are not equal.
Formula to calculate the image height is,
Here,
Substitute
From equation (6) and equation (9) respectively, substitute
Conclusion:
Therefore, the angle subtended is
(e)
Answer to Problem 36.27P
Explanation of Solution
Given info: The height of the following car is
Formula to calculate the angle subtended by the image,
Here,
Substitute
Conclusion:
Therefore, the image appears to be
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Chapter 36 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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