Question

A 1.1-m tall child is standing 6.0 m from a spherical convex mirror. The child’s image is 0.40 m behind the mirror. What is the image height and focal length of the mirror?

Answer 1

The image height is 0.36 m and the focal length of the mirror is approximately 0.35 m.

Step-by-step explanation:

To find the image height, we can use the magnification formula:

magnification = image height / object height

Given that the object height is 1.1 m and the image height is 0.40 m, we can plug in the values:

magnification = 0.40 m / 1.1 m = 0.36

Therefore, the image height is 0.36 m. To find the focal length of the mirror, we can use the mirror equation:

1/focal length = 1/object distance + 1/image distance

Given that the object distance is 6.0 m and the image distance is -0.40 m (using the sign convention for convex mirrors), we can plug in the values:

1/focal length = 1/6.0 m + 1/-0.40 m

Simplifying the equation, we find that the focal length of the mirror is approximately 0.35 m.

Answer 2

1 / i + 1 / o = 1 / f thin lens equation

(i + o) / o i = 1 / f

f = o i / (i + o) = 6 * -.4 / (-.4 + 6) = -2.4 / 5.6 = -.42 m

The focal length is -.42 m indicating a convex mirror

M = -I / O = -.4 / 6 = -.067 negative magnification indicates erect image

O = M * 1.1 = -.067 * 1.1 = -.073 m height of image

One must be careful with signs because they can vary with textbooks