Some distant star is to be observed by a tele | vedclass

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(D) The angular resolution $	heta$ of a telescope is given by the formula $	heta = 1.22 \frac{\lambda}{a}$,where $\lambda$ is the wavelength of ligh

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(D) The angular resolution $	heta$ of a telescope is given by the formula $	heta = 1.22 \frac{\lambda}{a}$,where $\lambda$ is the wavelength of light and $a$ is the diameter of the objective lens.Given: $	heta = 3.0 	imes 10^{-7}$ radian,$\lambda = 500 	ext{ nm} = 500 	imes 10^{-9} 	ext{ m}$.Rearranging the formula to solve for $a$: $a = \frac{1.22 \lambda}{	heta}$.Substituting the values: $a = \frac{1.22 	imes 500 	imes 10^{-9}}{3.0 	imes 10^{-7}} = \frac{610 	imes 10^{-9}}{3.0 	imes 10^{-7}} = 203.33 	imes 10^{-2} 	ext{ m} = 2.0333 	ext{ m}$.Converting to centimeters: $2.0333 	ext{ m} = 203.33 	ext{ cm}$.The nearest integer is $203 	ext{ cm}$. Note: Given the provided options,there appears to be a discrepancy in the question's expected range; however,based on the physics formula,the calculated value is $203 	ext{ cm}$.

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