In figure , L is half part of an equiconvex glass lens `(mu=1.5)` whose surfaces have radius of curvature R =40cm and its right surface is silvered . Normal to its principal axis a plane mirror M is placed on right of the lens . Distance between lens L and mirror M is b. A small object O is placed on left of the lens such that there is no parallax between final images formed by the lens and mirror. If transverse length of final image formed by lens is twice that of image formed by the mirror , calculate distance'a' in cm between lens and object.

Options

A. a = 2.5 cm
B. b = 5 cm
C. Distance of image from object is 15 cm
D. Image formed by silvered lens system is virtual

Answer

C, D

Explanation

`(2(a+b)-a)/(a)=2`
`{:(a+2b=2a,,2b=a),((1)/(f_(2))=(1.5-1)((2)/(40)),,f_(2)=40):}`
`f_(m)=-20`
`(1)/(F)=(1)/(f_(m))-(2)/(f_(2))f=-10cm`
`(1)/(V)+(1)/(u)=(1)/(F) a=5`
`(1)/(2a)+(1)/(-a)=(1)/(-10)b=2.5`