Two lenses have power of

(a) +2 D and

(b) -4 D

What is the nature and focal length of each lens?

(a) As we know,

$\text{Power} = \dfrac{1}{\text{focal length}}$

Given,

Power of the lens = +2.0 D

As the given power is positive,

Therefore, we can say that the lens used is convex in nature.

Substituting the value of power in formula we get,

$\text{2.0} = \dfrac{1}{\text{focal length}} \\[0.5em] \Rightarrow \text{focal length} = \dfrac{1}{2} \\[0.5em] \Rightarrow \text{focal length} = \text{0.5 m} \\[0.5em] \Rightarrow \text{focal length} = \text{50 cm} \\[0.5em]$

Therefore, the focal length is 50 cm and the lens used is convex in nature.

(b) As we know,

$\text{Power} = \dfrac{1}{\text{focal length}}$

Given,

Power of the lens = -4.0 D

As the given power is negative hence, we can say that the lens used is concave in nature.

Substituting the value of power in formula we get,

$-\text{4.0} = \dfrac{1}{\text{focal length}} \\[0.5em] \Rightarrow \text{focal length} = -\dfrac{1}{4} \\[0.5em] \Rightarrow \text{focal length} = -\text{0.25 m} \\[0.5em] \Rightarrow \text{focal length} = -\text{25 cm} \\[0.5em]$

Therefore, the focal length is 25 cm and the lens used is concave in nature.