Question

Two thin lenses, when in contact, produce a combination of power $+10D$. When they are $0.25m$ apart, the power reduces to $+6D$. The focal length of the lenses are:

• A. $20cm,30cm$
• B. $30cm,40cm$
• C. $12.5cm,50cm$
• D. $25cm,50cm$

Answer 1

Answer: (C)

$12.5cm,50cm$

$p=p_1+p_2$

$10=p_1+p_2$

$6=10-0.25p_1{p}_2$

$16=p_1{p}_2$

$(p_1-p_2{)}^2=(p_1+p_2{)}^2-4p_1{p}_2$

$=100-4\times 16=100-64=36$

$p_1-p_2=6$

$p_1+p_2=10$

$p_1=8$

$p_2=2$

$f_1=100/8=12.5cm$

$f_2=100/2=50cm$