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A Plano-convex lens of radius of curvature 0.1m is kept over a plane glass plate with curved surface of the lens touching it. The gap between the glass plate and the curved surface of the lens is filled with a liquid. If the combined focal length of the combination is 0.4m, calculate the refractive index of the material of the liquid. Given R.I. of the material of the lens is 1.5. |
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Answer» Solution :For plano-convex lens, R = 0.1m, `n_(1) = 1.5` `rArr(1)/( f_(1)) = ( n_(1) -1) ((1)/( R_(1)) - (1)/( R_(2)))` `(1)/(f_(1)) = ( 1.5 -1) ((1)/(0.1) - ( 1)/( oo)) = (0.5 )/(0.1)` `(1)/( f_(1)) = 5` or `f_(1) =0.2m` Also, COMBINED focal LENGTH `F = 0.4 m` `rArr (1)/(F) = (1)/( f_(1)) + ( 1)/( f_(2))` `(1)/(0.4) = ( 1)/( 0.2) + ( 1)/( f_(2))` `(1)/( f_(2)) = ( 1)/( 0.4) - (1)/( 0.2)` `= ( 10)/( 4) - ( 10)/( 2)` `(1)/( f_(2)) = ( 10-20)/( 4) = ( -10)/(4)` for lens formed by liquid FILLED in space. `(1)/(f_(2)) = ( n-1) ((1)/( R_(1)) - ( 1)/(R_(2)))` `- (10)/( 4) = ( n_(2) -1)((1)/( oo) - (1)/( 0.1))` `( - 10)/( 4) = ( -(n_(2)-1))/(0.1)` `( -10)/( 4) = (- ( n_(2) -1))/( 0.1)` `n_(2) -1 = (1)/( 4)` `n_(2) = 1+( 1)/( 4) = ( 5)/( 4) =1.25 ` |
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