Question

An image of the moon is focused onto a screen using a converging lens of focal length f= 34.3 cm. The diameter of the moon is 3.48×10^6 m, and its mean distance from the earth is 3.85×10^8 m. What is the diameter of the moon's image?

Answer 1

Answer:

The diameter of the moon's image is 0.31 cm.

Explanation:

Given that,

Focal length = 34.3 cm

Diameter of the moon $d=3.48\times10^{6}\ m$

Mean distance from the earth $d=3.85\times10^{8}\ m$

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

$m= \dfrac{image\ distance}{object\ distance}=\dfrac{height\ of\ image}{height\ of\ object}$

$\dfrac{0.343}{3.85\times10^{8}}=\dfrac{h'}{3.48\times10^{6}}$

$h'=\dfrac{0.343\times3.48\times10^{6}}{3.85\times10^{8}}$

$h'=0.0031\ m= 0.31\ cm$

Hence, The diameter of the moon's image is 0.31 cm.