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Two plano-convex lens of glass of refrac...

Two plano-convex lens of glass of refractive index 1.5 have radii of curvature 20cm and 30cm. They are placed in contact with curved surface towards each other and the space between them is filled with a liquid of refractive index `4/3`. Find the focal length of the system.

Text Solution

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As shown in the figure the system is equivalent to combination of three thin lenses in contact i.e., `1/F=1/f_1+1/f_2+1/f_3`
But by lens maker.s formula
`1/f_1=[3/2-1][1/(-infty)-1/20]=-1/40`
`1/f_2=[4/3-1][1/20+1/30]=5/180`
`1/(f_3)=[3/2-1][1/(-30)-1/(-infty)]=-1/60 so, 1/f=-1/40+5/180-1/60`
`i.e., 1/F=(-90+10-6)/360 or F=-72cm`
i.e., the system will behave as a divergent lens of focal length 72cm.
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