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(a) With the help of a labelled ray diagram, explain the construction and working of a Cassegrain reflecting telescope. (b) An amateur astronomer wishes to estimate roughly the size of the sun using his crude telescope consisting of an objective lens of focal length 200 cm and an eyepiece of focal length 10 cm. By adjusting the distance of the eyepiece from the objective, he obtains an image of the sun on a screen 40 cm behind the eyepiece. The diameter of the sun's image is measured to be 6.0 cm. Estimate the sun's Size, given that the average earth-sun distance is 1.5xx10^(11)m. |
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Answer» Solution :(b) For the eye piece `(1)/(u_(e))=(1)/(v_(e))-(1)/(f_(e))=(1)/(40)-(1)/(10)=(3)/(40)` `u_(e)=40//3cm` Magnification PRODUCED by the eye piece is `m_(e)=(v_(e))/(u_(e))=(40)/(40//3)=3` Diameter of the IMAGE formed by the objective is `D=6//3=2cm` IF D is the diameter of the sun then the angle substended by it on the objective will be `ALPHA=(D)/(1.5xx10^(11))" rad"` Now, angle subtended by the image at the objective = angle subtended by the sun `alpha=("size of image")/(f_(0))=(2)/(200)=(1)/(100)" rad"` Therefore, `(D)/(1.5xx10^(11))=(1)/(100)` `D=1.5xx10^(9)` |
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