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A convex lens is in contact with concave lens. If the ratio of their powers is 2/3 and focal length of the combination is 30 cm, then individual focal lengths are |
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Answer» 75 cm and -50 cm `P_1=1//f_1``P_2=1//f_2` Let `f_1` and `P_1` are the focal length and power of concave lens. `f_2` and `P_2` are the focal length and power of convex lens. The focal length of combined lens f = 30 cm Now, `(P_1)/(P_2)=(-2)/(3)` `THEREFORE(f_2)/(f_1)=(-2)/(3)` `implies f_2=-f_1xx2/3` ............(1) Now `1/f=(-1)/(f_1)+(1)/(f_2)` `(1)/(30)=(-1)/(f_1)+(3)/(2f_1)` (From eqn.1) `=(-1)/(2f_1)`[2+3] `impliesf_1=(-30)/(2)(5)=-15` cm Now,`f_2=-f_1xx2/3=(+15(2))/(3)=10` cm Hence `f_1=-15` cm,`f_2=10` cm |
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