Question

Two thin lenses have combined power of $10D$. When separated by $20cm$ their equivalent power is $6.25D$. Their individual powers in $D$ are

• A. $3.5$ and $6.5$
• B. $5$ and $5$
• C. $7.5$ and $2.5$
• D. $9.0$ and $1$

Answer 1

The correct option is C $7.5$ and $2.5$

Given that,

Power of combination $P=10D.....\left(I\right)$

Distance between lenses $d=20cm=0.2m$

Now, power of combination

$P^{\prime }=P_1+P_2-d(P_1+P_2)$

$6.25=10-0.2(P_1+P_2)$

$-0.2(P_1+P_2)=6.25-10$

$(P_1+P_2)=\frac{3.75}{0.2}$

$P_1+P_2=18.75$

Now,

${(P_1-P_2)}^2={(P_1+P_2)}^2-4P_1.P_2$

${(P_1-P_2)}^2=10\times 10-4\times 18.75$

${(P_1-P_2)}^2=25$

$(P_1-P_2)=5D......\left(II\right)$

Adding equation (I) and (2)

$P_1+P_2=10$

$P_1-P_2=5$

Now,

$2P_1=15$

$P_1=7.5D$

Now, put the value of $P_1$ in equation (I)

$P_2=10-7.5$

$P_2=2.5D$

Hence, the power of lenses $P_1=7.5D$ and $P_2=2.5D$