A bulb is located on a wall. Its image is to be obtained on a parallel with the help of a convex lens. If the distance between parallel walls is ' d ' then the required focal length of the l

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A bulb is located on a wall. Its image is to be obtained on a parallel with the help of a convex lens. If the distance between parallel walls is ' d ' then the required focal length of the lens placed in between the walls is:

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Since v + u = d ⇒ v = d − u From lens formula f 1 ​ ⇒ f 1 ​ ⇒ f ​ = v 1 ​ − u 1 ​ = d − u 1 ​ − − u 1 ​ = ( d − u ) u d ​ = d d u − u 2 ​ … ( i ) ​ Differentiating eq. (i) we have d u df ​ = d 1 ​ ( d − 2 u ) for maximum value of f 1 ​ = d u df ​ = 0 ​ ⇒ d 1 ​ ( d − 2 u ) = 0 ⇒ d = 24 ⇒ u = 2 d ​ ​ putting these value in eq. (i) f = 4 d ​

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