Two identical thin planoconvex glass lenses (refractive index `1.5)` each having radius of curvature of `20cm` are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index `1.7`. The focal length of the combination is

Options

A. `-25` cm
B. `-50` cm
C. 50 cm
D. `-20 ` cm

Answer

B

Explanation

`(1)/(f_(1)) = (1.5 - 1) ((1)/(infty) - (1)/(-20))`
`f_(1)` = 40 cm
`(1)/(f_(2)) = ((1.7 - 1)/(1)) (- (1)/(20) - (1)/(20))`
`f_(2) = (-100)/(7) cm , f_(3) = 40` cm
`therefore " " (1)/(f_("eq")) = (1)/(f_(1)) + (1)/(f_(2)) + (1)/(f_(3)) = (1)/(40) - (7)/(100) + (1)/(40)`
`rArr " " f_(eq) = -50` cm .