Question

An eye specialist prescribes spectacles having a combination of convex lens of focal length $40cm$ in contact with a concave lens of focal length $25cm$. The power of this lens combination is in dioptres,

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

Answer 1

The correct option is A

$-1.5D$

Step 1: Given Data-

the focal length of a convex lens is$f_1=40cm$_, as we know the focal length of the convex lens is always positive.

The focal length of the concave lens is$f_2=-20cm$_, as the focal length of concave lens is always negative.

Step 2: Calculate the focal length of the combination-

We know that Combined focal length$\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{f}$.

Therefore, $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{40}-\frac{1}{25}=\frac{-40+25}{40\times 25}=-\frac{3}{200}c{m}^{-1}=-1.5m^{-1}$

Step 3 Calculate power-

we know that power of the lens $P=\frac{1}{f}$

The power of the combination is $-1.5D$

Therefore, the correct option is (a) $-1.5D$.