The limit of resolution of a telescope is 3.0 | vedclass

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(A) The limit of resolution or angular resolution for a telescope is given by the formula: $\alpha_{\min} = \frac{1.22 \lambda}{D}$.Given values are:$

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$2.1$

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(A) The limit of resolution or angular resolution for a telescope is given by the formula: $\alpha_{\min} = \frac{1.22 \lambda}{D}$.Given values are:$\alpha_{\min} = 3.0 	imes 10^{-7} 	ext{ rad}$$\lambda = 525 	ext{ nm} = 525 	imes 10^{-9} 	ext{ m}$Rearranging the formula to solve for the diameter of the objective lens $(D)$:$D = \frac{1.22 \lambda}{\alpha_{\min}}$Substituting the values:$D = \frac{1.22 	imes 525 	imes 10^{-9}}{3.0 	imes 10^{-7}}$$D = \frac{640.5 	imes 10^{-9}}{3.0 	imes 10^{-7}}$$D = 213.5 	imes 10^{-2} 	ext{ m} = 2.135 	ext{ m}$.Rounding to the nearest given option, we get $D = 2.1 	ext{ m}$.

The limit of resolution of a telescope is $3.0 \times 10^{-7} \text{ rad}$. Assuming that it is used to see the light of wavelength $525 \text{ nm}$ from a star, what should be the diameter of the objective (in $\text{ m}$)?

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