Question

An eye specialist prescribes spectacles having combination of convex lens of focal length $40\text{cm}$ in contact with a concave lens of focal length $25\text{cm}$. The power of this lens combination in diopters is

• A. $+1.5$
• B. $-1.5$
• C. $+6.67$
• D. $-6.67$

Answer 1

The correct option is B $-1.5$


$f_1=+40\text{cm}=0.4\text{m}$
(for convex lens)
$f_2=-25\text{cm}=-0.25\text{m}$
(for concave lens)

Therefore, focal length $\left(f\right)$ of the combination,
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
$=\frac{1}{0.40}-\frac{1}{0.25}=\frac{0.25-0.4}{0.40\times 0.25}$
$=-\frac{0.15}{0.1}=-1.5D$
$\Rightarrow P=\frac{1}{f}=-1.5D$
(b) is the correct option.