The limit of resolution of a telescope is 2.5 | vedclass

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(A) The limit of resolution of a telescope is given by the formula: $\alpha = \frac{1.22 \lambda}{a}$, where $\alpha$ is the angular resolution, $\lam

Vedclass · Accepted Answer

$244$

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(A) The limit of resolution of a telescope is given by the formula: $\alpha = \frac{1.22 \lambda}{a}$, where $\alpha$ is the angular resolution, $\lambda$ is the wavelength of light, and $a$ is the diameter of the objective lens.Given values are $\alpha = 2.5 	imes 10^{-7} 	ext{ rad}$ and $\lambda = 500 	ext{ nm} = 500 	imes 10^{-9} 	ext{ m}$.Rearranging the formula for $a$: $a = \frac{1.22 \lambda}{\alpha}$.Substituting the values: $a = \frac{1.22 	imes 500 	imes 10^{-9}}{2.5 	imes 10^{-7}}$.$a = \frac{610 	imes 10^{-9}}{2.5 	imes 10^{-7}} = 244 	imes 10^{-2} 	ext{ m} = 2.44 	ext{ m}$.Converting to centimeters: $2.44 	ext{ m} = 244 	ext{ cm}$.Thus, the diameter of the objective lens is $244 	ext{ cm}$.

The limit of resolution of a telescope is $2.5 \times 10^{-7} \text{ rad}$. If the telescope is used to detect light of wavelength $500 \text{ nm}$ coming from a star, the diameter of the objective lens used by the telescope is: (in $\text{ cm}$)

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