Question

An eye specialist prescribes spectacles having combination of convex lens of focal length $40cm$ in contact with a concave lens of focal length $25cm$. 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 $-1.5$

$f_1=+40cm$ (for convex lens) $=0.4m$
$f_2=-25$ (for concave lens) $=-0.25m$
Therefore, focal length $\left(f\right)$ of the combination,
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
$=\frac{1}{0.40}-\frac{1}{0.25}=\frac{0.25-0.4}{0.40\times 0.25}$
$=-\frac{0.15}{0.1}=-1.5dioptre$.
$\Rightarrow P=\frac{1}{f}=-1.5dioptre$.
b. is the correct option.