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Units and Measurements — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements3 Marks
Question
Mars has approximately half of the earth’s diameter. When it is closest to the earth it is at about $\frac{1}{2}$ A.U. from the earth. Calculate what size it will appear when seen through the same telescope.
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Answer

Given that $\frac{\text{D}_\text{mars}}{\text{D}_\text{earth}}=\frac{1}{2}\ \ \ ...(\text{i})$ where D represents diameter. We know that, $\frac{\text{D}_\text{earth}}{\text{D}_\text{sun}}=\frac{1}{100}$ $\therefore\ \frac{\text{D}_\text{mars}}{\text{D}_\text{sun}}=\frac{1}{2}\times\frac{1}{100}$ [from Eq. (i)] At 1AU Sun's diameter $=\Big(\frac{1}{2}\Big)^\circ$ $\therefore$ Diameter of Mars $=\frac{1}{2}\times\frac{1}{200}=\Big(\frac{1}{400}\Big)^\circ$ At $\frac{1}{2}$AU, Mars' diameter $=\frac{1}{400}\times2^\circ=\Big(\frac{1}{200}\Big)^\circ$ With 100 magnification, Mars' diameter $=\frac{1}{200}\times100^\circ=\Big(\frac{1}{2}\Big)^\circ=30'$ This is larger than resolution limit due to atmospheric fluctuations. Hence, it looks magnified.

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