A concavo-convex lens has refractive index `1.5` and the radii of curvature of its surfaces are `10 cm and 20 cm.` The concave surface is upwords and is filled with oil of refractive index `1.6.` The focal length of the combination will be

Explanation

for the glass lens `(1)/(F) = (mu-1) [(1)/(R_1)-(1)/(R_2)]`
Here `R_1 = 10 cm , R_2 = 20 cm and mu = 1.5 `
` (1)/(f_1) = (1.5 -1) [(1)/(10 cm) - (1)/(20 cm)]=(1)/(40 cm )`
For the oil lens ` (1)/(f_2) =(mu-1) [(1)/(R_1) - (1)/(R_2)]`
Here ` R_1 = 20 cm R_2 = oo and mu =1.6 `
` (1)/(f ) = (1.6 -1) [(1)/(20 cm) - (1)/(oo)] = (3)/(100 cm)`
For the oil - glass combination
`(1)/(f) =(1)/(f_1) +(1)/(f_2) = (1)/(40 cm ) +(3)/( 100 cm ) =(11)/(200 cm )`
` therefore f=18.2 cm `