Given:
Diameter of the sphere (D sphere )=20 cm=0.20 m
Diameter of the moon ( D 1 ) =3,500 km=3,500,000 m
Distance from the moon to the sphere ( d 1 ) =384,000 km=384,000,000 m
To calculate the position of the image (d 2) and the diameter of the image ( D 2), we can use the concept of similar
triangles:
d 1 D1
=
d 2 D2
Let's solve for d 2 :
d 1 × D2
d 2=
D1
Substituting the given values:
384,000,000 m× D 2
d 2=
3,500,000 m
Now, let's calculate the diameter of the image ( D 2) using the diameter of the sphere (D sphere ):
D2=D sphere ×
( )
d2
D1
Substituting the given values:
D2=0.20 m× ( 3,500,000
d 2
m)
Now, substitute the expression for d 2 into the equation:
D2=0.20 m× ( 384,000,000 m×D
3,500,000 m ) 2
Distributing and simplifying:
0.20 m× 384,000,000 m× D 2
D 2=
3,500,000 m
Simplifying further:
0.20 ×384,000,000 1
1= 1=22.08 × D2 D 2= ≈ 0.045 m
3,500,000 22.08
Therefore, the diameter of the image of the moon in the polished sphere is approximately 0.045 meters.
To find the position of the image (d 2), substitute the value of D 2 into the earlier equation:
384,000,000 m× D 2 384,000,000 m ×0.045 m
d 2= ≈ ≈ 4000 m
3,500,000 m 3,500,000 m
Therefore, the position of the image of the moon inside the polished sphere is approximately 4000 meters from the
center of the sphere.
To recap:
The diameter of the image of the moon in the polished sphere is approximately 0.045 meters.
The position of the image of the moon inside the polished sphere is approximately 4000 meters from the
center of the sphere.
