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

Answer

1

Explanation

`1/f=(mu-1)(1/R_(1)-1/R_(2))`
= `(3/2 - 1)xx(1/20)=1/40`
(1,7-1)`xx(-1/20 - 1/20) = -7/100`
`1/f_(eq) = 1/f_(1) + 1/f_(2) + 1/f_(3)`
`(10+10-28)/400 = (20-28)/400`
= `-8/400 = -2/100 = -1/50`
`1/f_(eq)=1/f_(1) + 1/f_(2) + 1/f_(3)`
=`(10+10-28)/400 = 1/50`
`f_(eq)=-50`cm