Question

An eye specialist prescribes spectacles having a combination of a 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 Dioptre is:

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

Answer 1

The correct option is A $-1.5$

Focal length of convex mirror, $f_1=+40\text{cm}$
Focal length of concave mirror, $f_2=-25\text{cm}$

So, power of combination of lens,

$P=P_1+P_2=\frac{1}{f_1}+\frac{1}{f_2}$

$\Rightarrow P=\frac{1}{40}-\frac{1}{25}=\frac{25-40}{1000}$

$\Rightarrow P=\frac{-15}{1000}$

$\therefore$ power of combination will be

$P=\frac{-15}{1000}\times 100{\text{m}}^{-1}=-1.5\text{D}$

Hence, option $\left(a\right)$ is correct.