double -convex lens is to be manufactured from a glass of refractive index 1.55 with both faces of the same radius of curvatures . Calculate the radius of curvature required if the focal length is to be 20 cm ? Also find the focal length of the lens if it is immersed in water of refractive index 1.33 ?

Explanation

given :
`n_g =1.55 ,R = ? ,F=20 cm , R_I = + R ,R_2 =- R `
`(1)/(f) =(n_g-1)[(1)/(R_1)-(1)/(R_2)]`
`(1)/(20) = (1.55 -1) [1/R +1/R ]`
`=0.55 xx2/R`
`R=20 xx 0.55 xx 2`
` R =22 cm `
when the lens is immersed in water
`(1 )/(f_omega)=((n_g)/(n_omega)-1) [(1)/(R_1)-(1)/(R_2)]`
`(1)/(f_(omega) )= ((1.55)/(1.33)-1)[(1)/(22)+(1)/(22)]`
`(1)/(f_omega) =(1.1654 -1) 2/22`
`(1)/(f_omega)= 0.1654 xx(2)/(22)`
`(1)/(f_omega)=(0.3308)/(22)`
`f_(omega)=(22)/(0.3308)`
`f_(omega) = 66.5 cm `