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A Plano-convex lens of radius of curvatu...

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.

Text Solution

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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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