Ray Optics And Optical Instruments Ques 23
23. 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 ( $=1.5)$ as that of glass) then the equivalent focal length is $F_2$. The ratio $F_1: F_2$ will be:
[2019]
(a) $2: 1$
(b) $1: 2$
(c) $2: 3$
(d) $3: 4$
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Answer:
Correct Answer: 23.(b)
Solution:
- (b)
Equivalent focal length in air
$\frac{1}{F_1}=\frac{1}{f}+\frac{1}{f}=\frac{2}{f}$
$\Rightarrow F_1=\frac{f}{2}$ $\quad$ …….(i)
When glycerin is filled inside, it behaves like a concave lens of focal length (-f)
$\therefore \frac{1}{F_2}=\frac{1}{f}+\frac{1}{f}-\frac{1}{f} \quad \Rightarrow F_2=f$ $\quad$ …….(ii)
Dividing (i) by (ii), we get
$\frac{F_1}{F_2}=\frac{1}{2}$
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