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A screen is placed 90cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. Determine the focal length of the lens. |
Answer» Solution :`rArr` LET, image of object shown at O for combination of lenses `L_1` and `L_2` obtained at I.  `rArr` Here, clearly, `x+ 20 + x = 90 cm ` `therefore2 x = 70 ` `thereforex = 35 cm ` `rArr`x = 35 cm `rArr ` If lens is at `L_1`, thenObject distance u = -x = - 35 cm Image distance v = 20+ x = 20 + 35 = 55 cm `therefore` From lens formula `1/f = 1/v -1/u = 1/55- (1)/(-35) = (1)/(55) + (1)/(35)` `therefore 1/f = (7 + 11)/(385) = (18)/(385)` `therefore f = (385)/(18) = 21.4 cm ` Second METHOD : Distance between object and image D = 90 cm Distance between two lenses d = 20 cm Now `f= (D^2 - d^2)/(4D)` (this has to be remembered) `thereforef= ((90)^2 - (20)^2)/(4 xx 90) = (8100-400)/(360)` `therefore f = (7700)/(360) = 21.38 cm ` `thereforef ~~ 21.4 cm ` |
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