The outside mirror on the passenger side of a car is convex and has a focal length of -7.2 cm. Relative to this mirror, a truck traveling in the rear has an object distance of 20 m. Find (a) the image distance and (b) the magnification of the mirror.
To find the image distance and magnification of the convex mirror, we can use the mirror equation and the magnification formula.
(a) The mirror equation is given by:
1/f = 1/o + 1/i
Where:
f is the focal length of the mirror (given as -7.2 cm)
o is the object distance (given as 20 m)
i is the image distance (unknown)
First, let's convert the units of the object distance to match the focal length. The object distance is given in meters, so let's convert it to centimeters:
o = 20 m * 100 cm/m = 2000 cm
Now we can rearrange the mirror equation to solve for the image distance:
1/i = 1/f - 1/o
1/i = 1/-7.2 - 1/2000
1/i = -0.13888 - 0.0005
1/i = -0.13938
i = 1 / -0.13938
i ≈ -7.17 cm
So, the image distance is approximately -7.17 cm.
(b) The magnification of a mirror is defined as the ratio of the height of the image (hi) to the height of the object (ho). It can also be calculated using the formula:
magnification (m) = -i / o
Where:
m is the magnification (unknown)
i is the image distance (-7.17 cm)
o is the object distance (2000 cm)
Substituting the given values, we get:
m = -(-7.17 cm) / 2000 cm
m = 7.17 / 2000
m ≈ 0.0036
So, the magnification of the mirror is approximately 0.0036.