Two plano concave lenses of glass of refractive index 1.5 has radii of curvature 20cm and 30cm

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A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of a focal length 20 cm, and (b) a concave lens of focal length 16 cm?

Here, the point P on the right of the lens acts as a virtual object.

Object distance, u = 12 cm

∴           1v =120+112      =3+560 =860

i.e.,           v = 60/8 = 7.5 cm. 

Image is at a distance of 7.5 cm to the right of the lens, where the beam converges. (b)Now,Focal length of concave lens, f = –16 cmObject distance, u = 12 cm 

⇒      v = 48 cm 

Hence, the image is at a distance of 48 cm to the right of the lens, where the beam would converge.

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Tw9 planoconcave lenses of glass of refractive index 1.5 have radii of curvature of 20cm and 30cm.They are placed in contact with curved surfaces towards each other and space between them is filled with liquid(u=4/3).focal length of the system is

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