Question

Figure A shows two identical plano-convex lenses in contact as shown.The combination has local length 24 cm.Figure B shows the same with a liquid introduced between them.If refractive index of glass of the lenses is 1.50 and that of the liquid is 1.60 , the focal length of the system in figure B will be

• A. -120 cm
• B. -24 cm
• C. 120 cm
• D. 24 cm

Answer 1

Answer: (A)

Let radius of the convex side be $R$.

By lens makers' formula,

So focal length of 2 identical plano-convex lens is given by, $\frac{1}{f}=\frac{1}{24}=(1.5-1)(\frac{1}{\infty }-\frac{1}{-R})+(1.5-1)(\frac{1}{R}-\frac{1}{\infty })⟹R=24cm$

The total focal length of the lens combination can be given as,

$\frac{1}{f_t}=(1.5-1)(\frac{1}{\infty }-\frac{1}{-R})+(1.6-1)(\frac{1}{-R}-\frac{1}{R})+(1.5-1)(\frac{1}{R}-\frac{1}{\infty })$

$⟹\frac{1}{f_t}=\frac{-0.2}{R}⟹f_t=-120cm$

Option A is correct