As shown in figure a spherical air lens of radii R_1=R_2=10cm is cut in a glass cylinder. Determine the focal length and nature of air lens. IF a liquid of refractive index 2 is filled in the lens, what will happens to its focal length and nature?

As shown in figure a spherical air lens of radii R_1=R_2=10cm is cut i

1.	As shown in figure a spherical air lens of radii R_1=R_2=10cm is cut in a glass cylinder. Determine the focal length and nature of air lens. IF a liquid of refractive index 2 is filled in the lens, what will happens to its focal length and nature?
Answer» Solution :ACCORDING to lens MAKER formula, `1/f=(mu-1) [1/R_1-1/R_2]` with `mu=mu_1/mu_2` Intially `mu=mu_a/mu_u=1/((3//2))=2/3, R=+10 cm and R_2=-10cm` So `1/f=[2/3-1][1/(+10)-1/(-10)]=-2/30 i.e., f=-15 cm` i.e. the air lens in glass behaves as divergent lens of focal LENGTH 15 cm When the liquid of `mu=2` is filled in the air CAVITY. `mu=mu_1/mu_u=2/1.5=4/3` So that now `1/f.=[4/3-1][1/10-1/10]=2/30` f.=15CM i.e., the liquid lens in glass will behaves as a convergent lens of focal length 15cm.