Question

An optician prescribes spectacles to a patient with a combination of a convex lens of focal length $40cm$ and concave lens $25cm$. The power of spectacles is:

• A. 6.0 D
• B. 1.5 D
• C. -6.0 D
• D. -1.5 D

Answer 1

Answer: (D)

Power of a lens is equal to inverse of its focal length.
The power of a thin lens is equal to the reciprocal of its focal length $(f)$ measured in meters
$P=\frac{1}{f\text{ (meters) }}$
Given, focal length of convex lens $f_1=40cm$
and of concave lens $f_2=-25cm$
$\therefore$ Focal length of combination
$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$
$=\frac{1}{40}-\frac{1}{25}=-\frac{3}{200}$
$\Rightarrow F=-\frac{200}{3}=-66.7cm$
Power of spectacles is
$=\frac{100}{F}=\frac{100}{-66.7}=-1.5D$