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Calculate the separation of two points o...

Calculate the separation of two points on moon that can be resolve using `600 cm` telescope. Given distance of moon from earth `= 3.8 xx 10^(10) cm`. The wavelength most sensitive to eye is `5.5 xx 10^(-5) cm`.

Text Solution

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Here, `x = ? D = 600 cm`,
`lambda = 5.5 xx 10^(-5) cm`
Limit of resolution, ,brgt `dphi = (1.22 lambda)/(D) = (1.22 xx 5.5 xx 10^(-5))/(600)`
`= 1.1 xx 10^(-7) rad`.
If `x` is separation of two points on the moon that can be resolved and `d` is distance of moon from objective of telescope, then `dphi = (x)/(d)`,
`x = (dphi) d = 1.1 xx 10^(-7) xx 3.8 xx 10^(10) cm`
`= 4180 cm`
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