Question

Two thin lenses, when in contact, produce a combination of power $+10D$. When they are $0.25m$ apart, the power is reduced to $+6D$. The power of the lenses in dioptres, are

• A. 1 and 9
• B. 2 and 8
• C. 4 and 6
• D. 5 each

Answer 1

Answer: (B)

Case I When lenses are in contact, $P=\frac{1}{F_1}=+10D$
$\frac{1}{F_1}=\frac{1}{f_1}+\frac{1}{f_2}$
$\Rightarrow 10=\frac{1}{f_1}+\frac{1}{f_2}$
Case II When lenses are $d=0.25m$ apart
$P=\frac{1}{F_2}=+6D$
$\Rightarrow \frac{1}{F_2}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}\dots (ii)$
From Eq. (i),
$6=10-\frac{0.25}{f_1{f}_2}$
or $f_1{f}_2=\frac{0.25}{4}=\frac{1}{16}$
$\Rightarrow \frac{1}{f_1}\times \frac{1}{f_2}=16$
$\therefore P_1{P}_2=16...(iii)$
Hence, from Eq. (iii), only option (b) satisfies this relation.
Hence $P_1$ and $P_0$ is $2$ and $8$ .