Question

the image of the moon is formed by the concave mirror whose radius of curvature is 4.8m at a time when distance from the moon is 2.4 x 10^8. if the diameter of the image is 2.2 cm, the diameter of moon is

Answer 1

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Answer 2

Given: radius of curvature is 4.8m of the concave mirror, distance from the moon is 2.4 x 10^8, the diameter of the image is 2.2 cm

To find: the diameter of the moon

Solution: we are given the radius of curvature of the mirror

so the focal length of the mirror will be R/ 2

f = - 4.8/2 = - 2.4m

here will be assume that the distance of the object that is the moon from the mirror will be infinite

Therefore, the image formed of the moon will be the principal focus of the concave mirror.

So, v= f = -2.4m

we know that magnification m = - v/u = h2/h1

here v is a distance of the image from the mirror

u is distance of the object from the mirror

h1 is height of the object

h2 is height of the image

putting the values, we will get

height of the object that is moon = diameter of the moon = (- 2.2×10^-2)/ -(-2.4)(-2.4 ×10^8) = +2.2×10^6m.

The diameter of the moon will be  2.2 ×10^6 m