Two similar thin equi-convex lenses of focal length $f$ each are kept coaxially in contact with each other, such that the focal length of the combination is $F_1.$ When the space between the two lenses is filled with glycerin (which has the same refractive index ($\mu =1.5$) as that of glass), then the equivalent focal length is $F_2.$ The ratio $F_1:F_2$ will be

• A

  $2:1$
• Correct answer
  B

  $1:2$
• C

  $2:3$
• D

  $3:4$

Solution

Case I:

$\frac{1}{F_{\mathrm{eq}}}+\frac{1}{F}+\frac{1}{F}$
$F_1=F_{\mathrm{eq}}=\frac{F}{2}$
Case II:

$F_2=F_{\mathrm{eq}}=F$
$F_1:F_2=1:2$

Hence, the correct answer is option: 'B'.