Question

An optician prescribes spectacles to a patient with a combination of a convex lens of focal length 40 cm and a concave lens of focal length 25 cm. What will be the power of spectacles?

• A. 1.5 D
• B. 1.5 D
• C. -1.5 D
• D. -2.5 D

Answer 1

The correct option is C -1.5 D

Focal length of the convex lens ($f_A$) = 40 cm = 0.4 m​

Focal length of the concave lens ($f_B$) = -25 cm = - 0.25 m​

Power of a lens (P) = $\frac{1}{f}$
$P_A$ = $\frac{1}{f_A}$ = $\frac{1}{0.4m}$ = 2.5 D

$P_B$ = $\frac{1}{f_B}$ = $\frac{1}{-0.25m}$ = -4 D

Combined power of spectacles with both the lenses = $P_A$ + $P_B$​
= 2.5 D + (-4 D) ​
= - 1.5 D​

​Power of spectacles having both the given lenses is -1.5 D​