Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contact with their curved surface towards each other and the space betweent hem is filled with liquid of refractive index `(4)/(3)` the the combination is

Options

A. Convex of focal length 70 cm
B. Concave of focal length 70 cm
C. Concave of focal length 66.6 cm
D. Convex of focal length 66.6 cm

Answer

C

Explanation

`(1)/(f_(eq)) = (1)/(f_(1)) + (1)/(f_(2)) + (1)/(f_(3)) `
Using Lens maker.s formula,
`(1)/(f_(1)) = ((3)/(2) - 1) ((1)/(infty) - (1)/(25) ) = - (1)/(50)`
`(1)/(f_(2)) = ((4)/(3) - 1) ( (1)/(25) + (1)/(20) ) = (3)/(100)`
`(1)/(f_(3)) = ( (3)/(2) - 1) (- (1)/(20) - (1)/(infty) ) = - (1)/(40)`
`therefore (1)/(f_(eq)) = -(1)/(50) + (3)/(100) - (1)/(40)`
`therefore (1)/(f_(eq)) = -(1)/(50) + (3)/(100) - (1)/(40)`
`f_(eq) = - 66.6 `cm
System behaves as a concave lens of focal length 66 6. cm.