Two lenses have the power of +2D and –4D. What is the nature and focal length of each lens?

The lens with the power

+ 2 D

is convex with a focal length of

50 cm

, whereas the lens with the power

- 4 D

is concave with a focal length of

- 25 cm

.
The power of the lens is defined as the reciprocal of focal length in meters.
Given,
Power,

P_{1} = + 2 D

Power,

P_{2} = - 4 D

Power of convex lens is positive

P_{1} = \frac{1}{f_{1}}

\Rightarrow + 2 = \frac{1}{f_{1}}

\Rightarrow

f_{1} = \frac{1}{+ 2}

\Rightarrow f_{1} = + 0.5 m

\Rightarrow

f_{1} = + 50 cm

Power of concave lens is negative

P_{2} = \frac{1}{f_{2}}

\Rightarrow - 4 = \frac{1}{f_{2}}

\Rightarrow

f_{2} = \frac{1}{- 4}

\Rightarrow

f_{2} = - 0.25 m

\Rightarrow

f_{2} = - 25 cm

Two lenses have the power of $+ 2 D$ and $- 4 D$ . What is the nature and focal length of each lens?