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

Two plano concave lens of glass of refractive index 1.5 have radii of

1.	Two plano concave lens of glass of refractive index 1.5 have radii of curvature of 20 and 30 cm. They are placed in contact with curved surfaces towards each other and the space between them is filled with a liquid of refractive index (4//3). Find the focal length length of the system.
Answer» Solution :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.