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GUJCET · Physics · Ray Optics and Optical Instruments
If the tube length of astronomical telescope is \(\mathbf{9 6} \mathbf{~ c m}\) and magnifying power is \(\mathbf{1 5}\) for normal setting then the focal length of the objective is ________ cm.
- A 92
- B 105
- C 90
- D 100
Answer & Solution
Correct Answer
(C) 90
Step-by-step Solution
Detailed explanation
(C) 90
\(m=\frac{f_{0}}{f_{e}}=15\)
\(\therefore f_{e}=\frac{f_{0}}{15}\)
Now, \(f_{0}+f_{e}=96\)
\(\therefore f_{0}+\frac{f_{0}}{15}=96\)
\(\therefore \quad \frac{16 f_{0}}{15}=96\)
\(\therefore \quad f_{0}=\frac{15 \times 96}{16}\)
\(\therefore \quad f_{0}=90 \mathrm{~cm}\)
\(m=\frac{f_{0}}{f_{e}}=15\)
\(\therefore f_{e}=\frac{f_{0}}{15}\)
Now, \(f_{0}+f_{e}=96\)
\(\therefore f_{0}+\frac{f_{0}}{15}=96\)
\(\therefore \quad \frac{16 f_{0}}{15}=96\)
\(\therefore \quad f_{0}=\frac{15 \times 96}{16}\)
\(\therefore \quad f_{0}=90 \mathrm{~cm}\)
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