1) Some rearview mirrors produce images of cars to your rear that are smaller th
ID: 2299108 • Letter: 1
Question
1) Some rearview mirrors produce images of cars to your rear that are smaller than they would be if the mirror were flat.
What is a mirror's radius of curvature if cars 15.0m away appear 0.37 their normal size? Follow the sign conventions.
Express your answer to two significant figures and include the appropriate units.
2) In searching the bottom of a pool at night, a watchman shines a narrow beam of light from his flashlight,1.3?m above the water level, onto the surface of the water at a point d = 2.9m from his foot at the edge of the pool
Where does the spot of light hit the bottom of the h = 2.4-m-deep pool? Measure from the bottom of the wall beneath his foot.
Express your answer to two significant figures and include the appropriate units.
Explanation / Answer
distance of object u = 15 m
magnification m = 0.37
i.e., v / u = 0.37
v = 0.37 * 15 m
= 5.55 m
where v = distance of image
from the relation ( 1/ u )+ ( 1/ v ) = ( 1/ f)
from this you find focal lengthg of the mirror ( f ).
radius of curvature of the mirror R = 2 f
substittue values we get answer
This problem takes advantage of one of the properties of light as it crosses between two different mediums: refraction.
First we need to find what angle the light hits the surface of the water. To do this we construct a right triangle with 1.3 m as its height and 2.9 m as its length. We find the angle a to be equal to arctan(1.3/2.9) = .421 radians.
Next we use the equation for refraction, using the index of refraction (Na) of air to be about 1.000 and index of refraction of water (Nw) to be about 1.333.
sin(?a) x Na = sin(?w) x Nw
sin(.421) x 1.000 = sin(?w) x 1.333
?w = .306 Radians from the perpendicular.
Now we construct yet another right triangle using this angle as well as the 2.4 meters given to us in the problem, which we'll use as the height.
tan(.306) = 2.4/d
d = 2.4 / tan(pi/2 - .306) = 7.59 m from where the light entered the water originally. So the distance from the edge of the pool is 3m + 7.59m = 10.59 m
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