Question

1. The radius of Earth is 6.40 x 10° km. The moon is about 3.84 × 10' km away

from Earth and has a diameter of 3475 km. The Pacific Ocean surface, which
can be considered a convex mirror, forms a virtual image of the moon. What is
the diameter of that image?

Answer 1

Answer: 28.71 km

Step-by-step explanation:

For the convex mirror (ocean):

Radius of curvature = 6.4*10^3 km

Focal length (f) = R/2 = 3.2*10^3 km

Object distance (u) = -3.84*10^5

Mirror formula:
`(1)/(u) + (1)/(v) = (1)/(f)`

`(1)/(u) + (1)/(v) = (1)/(f)`

`(-1)/(3.84*10^5) + (1)/(v) = (1)/(3.2*10^3)`

v = 3173.55km

Magnification,
`m = (-v)/(u) = (-3173.55)/(-3.84*10^5) = (h_(i) )/(h_(o) )`

So, height of image/height of object = 3173.55/3.84*10^5

Diameter of image = 3173.55/3.84*10^5 * 3475

Diameter of image = 28.71 km

Therefore, the diameter of the image is 28.71 km