Question

A convex lens of power 5 D and a concave lens of power 7.5 D are placed in contact with each other. Which of the following is/are correct regarding the combination of these lens.

• A. Power of combination of lens is 12.5 D
• B. Power of combination of lens is -2.5 D
• C. Focal length of the combination of lens is 8 cm
• D. Focal length of the combination of lens is -40 cm

Answer 1

Answer: (B), (D)

The correct options are
B Power of combination of lens is -2.5 D
D Focal length of the combination of lens is -40 cm

Let $P$ represents power of lens and $f$ represents focal length of lens.
Given: Power of convex lens, $P_1=5D$
Power of concave lens, $P_2=-7.5D$ (power of concave lens is taken as negative)
So power of combination of lens = $P_{total}$
$P_{total}$ = $P_1$ + $P_2$ = +5 + (-7.5)
$P_{total}$ = -2.5 D
Since we know that P = $\frac{1}{f\left(inmetre\right)}$
$\Rightarrow f=\frac{1}{P}$$=\frac{1}{-2.5}=-0.4m=-40cm$