The spherical side mirror on a car is convex and has a radius of curvature of 25 cm. Another car is following, 20 m behind the mirror. If the height of the car is 1.6 m, how tall is its image?

f=-R/2; f=-25/2; f=-12.5

1/do+1/di=1/f
1/2000+1/di=1/-12.5
.0005+1/di=-.08
1/di=-0.0805
di=-12.42cm

1.6*di/do=1.6*2000/-12.42=-0.0099=1 cm

To find the height of the image, we can use the magnification formula for a thin lens or mirror:

magnification (m) = -image height (h') / object height (h)

For a convex mirror, the magnification is always positive and less than 1. Therefore, we can rewrite the formula as:

magnification (m) = image height (h') / object height (h)

Given:
Radius of curvature (R) = 25 cm = 0.25 m
Object distance (u) = -20 m (since the object is behind the mirror)
Object height (h) = 1.6 m

To calculate the image height (h'), we need to solve for the magnification (m) using the mirror equation:

1/f = 1/u + 1/v

where f is the focal length of the mirror and v is the image distance.

Since the mirror is convex, the focal length is half the radius of curvature:

f = R / 2 = 0.25 / 2 = 0.125 m

Plugging in the given values into the mirror equation:

1/0.125 = 1/-20 + 1/v

1/v = 1/0.125 + 1/20
1/v = 8 + 0.05
1/v = 8.05
v = 1 / 8.05
v ≈ 0.124 m

Now, we can find the magnification (m):

m = v / u
m = 0.124 / -20
m ≈ -0.0062

Finally, we can calculate the image height (h'):

m = h' / h
-0.0062 = h' / 1.6
h' = -0.0062 * 1.6
h' ≈ -0.00992 m

Since the height of an image cannot be negative, the image height is approximately 0.00992 m.

To find the height of the car's image, we can use the magnification formula for concave mirrors, which is given by:

magnification (m) = height of image (h') / height of object (h)

In this case, we are dealing with a convex mirror, but the magnification formula is the same. Keep in mind that the magnification for a convex mirror is always positive, indicating an upright and reduced image.

Now, let's find the magnification first:

magnification (m) = -d’ / d

where d’ is the distance between the mirror and the image and d is the distance between the mirror and the object.

In this scenario, the object is the car, and the image is formed by the mirror. The distance between the mirror and the car (d) is 20 m, and the radius of curvature of the mirror is 25 cm (0.25 m). Since the image formed by a convex mirror is virtual, the distance between the mirror and the image (d') is the same as the distance between the mirror and the object (d), i.e., 20 m.

Now, let's calculate the magnification:

magnification (m) = -d' / d = -20 m / 20 m = -1

Since the magnification is -1, it means that the height of the image (h') is equal to the negative height of the object (h) multiplied by the magnification.

height of image (h') = -height of object (h) * magnification (m)

Given that the height of the car (object) is 1.6 m, we can calculate the height of the image:

height of image (h') = -1.6 m * -1 = 1.6 m

Therefore, the height of the car's image is also 1.6 meters.

1/do+1/di=1/f is the equation, solve for di.

then, having di (remember the sign conventions for convex mirrors),

M=-di/do=hi/ho