The image of a distant tree is virtual and very small when viewed in a curved mirror. the image appears to be 22.9 cm behind the mirror. what kind of mirror is it?
what is its radius of curvature? (in cm)

45.8 cm

Explanation:

distance of object from the mirror is infinity

distance of image, v = 22.9 cm

The mirror is convex because it is used to see the distant objects and the image formed by the mirror is erect and small.

use mirror formula

Let f be the focal length of the mirror

1 / f = 1 / v + 1 / u

1 / f = 1 / 22.9  + 1 / ∞

f = 22.9 cm

radius of curvature = 2 x focal length

radius of curvature = 2 x 22.9 = 45.8 cm

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.