Respuesta :
Answer:
The diameter of the moon's image is 0.31 cm.
Explanation:
Given that,
Focal length = 34.3 cm
Diameter of the moon [tex]d=3.48\times10^{6}\ m[/tex]
Mean distance from the earth [tex]d=3.85\times10^{8}\ m[/tex]
At that distance the object is assumes to be at infinity. hence the image will be formed at a distance equal to focal length
So, the image distance is 34.3 cm.
We need to calculate the diameter of the moon's image
Using formula of magnification
[tex]m= \dfrac{image\ distance}{object\ distance}=\dfrac{height\ of\ image}{height\ of\ object}[/tex]
[tex]\dfrac{0.343}{3.85\times10^{8}}=\dfrac{h'}{3.48\times10^{6}}[/tex]
[tex]h'=\dfrac{0.343\times3.48\times10^{6}}{3.85\times10^{8}}[/tex]
[tex]h'=0.0031\ m= 0.31\ cm[/tex]
Hence, The diameter of the moon's image is 0.31 cm.
The diameter of the moon's image is 0.31 cm.
What is Diameter?
This is defined as the length of the line through the center that touches two points on the edge of the circle.
Parameters
Focal length = 34.3 cm
Diameter of the moon (d) = 3.48×10⁶ m
Mean distance from the earth = 3.85×10⁸ m.
The object is at infinity at that distance so the image formed will have a distance equal to focal length.
Image distance = 34.3 cm.
Diameter of the moon's image = ?
Magnification = image distance/object distance = height of image/height of object
0.343 / 3.85×10⁸ = hi / 3.48×10⁶
hi = 0.343 × 3.48×10⁶ / 3.85×10⁸
= 0.0031m = 0.31cm
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