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Some distant star is to be observed by some telescope of diameter of objective lens $$a$$, at an angular resolution of $$3.0 \times 10^{-7}$$ radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is __________ cm. (nearest integer)
Correct Answer: 203
Use Rayleigh criterion for telescope:
$$\theta=1.22\frac{\lambda}{D}$$
given:
$$θ=3.0\times10^{-7},λ=500nm=5\times10^{-7}m$$
$$D=\frac{1.22\lambda}{\theta}=\frac{1.22\times5\times10^{-7}}{3\times10^{-7}}$$
$$=\frac{6.1}{3}\approx2.03m$$
convert to cm:
2.03 m=203 cm
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