if `mu_2=._au_g=(3)/(2),mu_3=._au_(omega)=(4)/(3)`, magnitude of radii of carvature of lens are 10 cm and 20 cm find focal length of lens if rays are incident from (a) air and (b) water,

Explanation

(a) If rays are incident from air side
`mu_1=1,mu_2=``_au_g=(3)/(2),mu_3=``_au_(omega)=(4)/(3),R_1=10cm,R_2=-20cm`
`(mu_3)/(f_2)=(mu_2-mu_2)/(R_1)+(mu_3-mu_2)/(R_2)`
`((4)/(3))/(f_2)=((3)/(2)-1)/(10)+((4)/(3)-(3)/(2))/(-20)=(1)/(20)+(1)/(120)=(7)/(120)`
`(4)/(3f_2)=(7)/(120)impliesf_2=(160)/(7)cm`
(b). If rays are incident from water side
`mu_1=``_au_(omega)=(4)/(3),mu_2=``_au_g=(3)/(2)`
`mu_3=1,R_1=20cm,R_2=-10cm`
`(mu_3)/(f_1)=(mu_2-mu_1)/(R_1)+(mu_3-mu_2)/(R_2)`
`(1)/(f_1)=((3)/(2)-(4)/(3))/(20)+(1-(3)/(2))/(-10)`
`=(1)/(120)+(1)/(20)=(7)/(120)`
`f_1=(120)/(7)cm`