Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year $= 9.46 \times 10^{15} m$ ) of the order of:

Question

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year

= 9.46 \times 10^{15} m

) of the order of:

Toppr Admin · Accepted Answer

We have- -x394-x3B8-0-61-x3BB-9-lRl-R90-61-xD7-x3BB-9-46-xD7-1015-xD7-10-xD7-0-61-xD7-600-xD7-10-x2212-90-3-1-15-xD7-1011m-1-115-xD7-108km

We have, Δθ=0.61λ9=lRl=R90.61×λ=9.46×1015×10×0.61×600×10−90.3=1.15×1011m=1.115×108km

We have, $Δ θ = \frac{0.61 λ}{9} = \frac{l}{R}$

$l = \frac{R}{9} 0.61 \times λ$

$= \frac{9.46 \times 10^{15} \times 10 \times 0.61 \times 600 \times 10^{- 9}}{0.3}$

$= 1.15 \times 10^{11} m$

$= 1.115 \times 10^{8} k m$