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Two refracting telescopes are used to look at craters on the Moon. The objective focal length of both telescopes is $95.0 \mathrm{~cm}$ and the eyepiece focal length of both telescopes is $3.80 \mathrm{~cm}$. The telescopes are identical except for the diameter of the lenses. Telescope A has an objective diameter of $10.0 \mathrm{~cm}$ while the lenses of telescope B are scaled up by a factor of two, so that its objective diameter is $20.0 \mathrm{~cm}$. a) What are the angular magnifications of telescopes $A$ and $B$ ? b) Do the images produced by the telescopes have the same brightness? If not, which is brighter and by how much?

Solution

Verified**Given**
The focal lengths of the objective lenses of both telescopes are the same: $f_{oA}=f_{oB}=f_o=95\ \text{cm}$.
The focal lengths of the eyepieces of both telescopes are the same: $f_{eA}=f_{eB}=f_e=3.8\ \text{cm}$.
The diameters of the objective lenses of telescopes A and B are, respectively: $d_A=10\ \text{cm}$ and $d_B=20\ \text{cm}$.

It is required of us to find the angular magnifications of the telescopes $m_A$ and $m_B$ and the ratio of brightness for both telescopes.

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