Two identical thin planoconvex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex sufaces 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. `-20cm`
B. `-25cm`
C. `-50cm`
D. 50cm

Answer

C

Explanation

(c ) Given, `mu_(g)=1.5`
`mu_(oil)=1.7`
and R=20 cm
From Len's makers formula for the plano-convex lens,
`1/f=(mu-1)[1/R_(1)-1/R_(2)]`
Here, `R_(1)= R` and for plane surface, `R_(2)=oo`
`therefore 1/(f_("lens"))=(1.5-1)(1/R-0)rArr1/(f_("lens"))=0.5R`
When the interveining medium is fill with oil, then focal length of the concave lens formed by the oil
`1/(f_(concave))=(1.7-1)(-1/R-1/R)=-0.7xx2/R=(-1.4)/R`
Here, we have two concave surfaces.
So, `1/(f_(eq))=2xx1/(f_(l))+1/(f_(e))=2xx0.5/R+((-1.4)/R)=1/R=1.4/R=-0.4/R`
Focal length of the combination,
`therefore f_(eq)=-R/0.4=-20/0.4=-50 cm`