Optics 3 Question 29
29. Two thin lenses, when in contact, produce a combination of power $+10 D$. When they are $0.25 m$ apart, the power reduces to $+6 D$. The focal length of the lenses are …… $m$ and ……m.
(1997, 2M)
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Answer:
Correct Answer: 29. $0.125,0.5$
Solution:
- When the lenses are in contact, the power of the system is
$$ P=P _1+P _2 \text { or } P _1+P _2=10 $$
When lenses are separated by a distance $d=0.25 m=\frac{1}{4} m$
The power is $P=P _1+P _2-d P _1 P _2$
or $\quad P _1+P _2-\frac{P _1 P _2}{4}=6$
Solving Eqs. (i) and (ii), we can find that $P _1=8 D$ and $P _2=2 D$
$$ \begin{array}{ll} \therefore & f _1=\frac{1}{8} m=0.125 m \\ \Rightarrow & f _2=\frac{1}{2} m=0.5 m \end{array} $$
