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Wave Optics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsWave Optics2 Marks
Question
The minimum angular reparation between two stars is \(4 \times 10^{-6} rad\), if telescope is used to observe them with an objective of aperture \(16 cm\). Find the wavelength of light used.
✓

Answer

$d\theta = 4 \times 10^{−6} rad, a = 16 cm = 16 \times 10^{−2} m$
\(d \theta=\frac{1.22 \lambda}{ a }\)
\(\lambda=\frac{ d \theta \times a }{1.22}\)
\(=\frac{4 \times 16 \times 10^{-8}}{1.22}\)
\(=\frac{64 \times 10^{-8}}{1.22}\)
\(=(\log (64)-\log (1.22)) \times 10^{-8}\)
\(=(1.8062-0.0864) \times 10^{-8}\)
\(=(\operatorname{antilog}(1.7198)) \times 10^{-8}\)
\(=52.46 \times 10^{-8} m\)
$=5246Å$
The wavelength of light used is 5246 Å.

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