Question

A doctor prescribed a corrective lens of power \(+1.5\text{ D}\). Determine the focal length of the lens. Is the prescribed lens diverging or converging?

Hint:

Positive Power (\(+\text{D}\)) \(\rightarrow\) Convex Lens \(\rightarrow\) Converging Lens \(\rightarrow\) Corrects Hypermetropia.
Negative Power (\(-\text{D}\)) \(\rightarrow\) Concave Lens \(\rightarrow\) Diverging Lens \(\rightarrow\) Corrects Myopia.

Answer 1

Step 1: Understanding the Concept:
The power of a lens is the reciprocal of its focal length expressed in meters.

Step 2: Key Formula or Approach:
Power \(P = \frac{1}{f(\text{in meters})}\)

Step 2: Detailed Explanation:
Given Power, \(P = +1.5\text{ D}\) (Diopters).
To find focal length \(f\):
\[ f = \frac{1}{P} \] \[ f = \frac{1}{+1.5}\text{ meters} \] Converting to centimeters:
\[ f = \frac{100}{1.5}\text{ cm} \] \[ f = \frac{1000}{15}\text{ cm} \] \[ f = 66.67\text{ cm} \] The positive sign of the power and focal length indicates that the lens is convex.
A convex lens converges light rays.
Therefore, it is a converging lens.

Step 3: Final Answer:
The focal length is \(66.67\text{ cm}\) and it is a converging lens.