Question

Calculate the focal length of a lens with power –2.0 D and identify its type.

Hint:

If the power of a lens is {positive}, the lens is {convex}. If the power of a lens is {negative}, the lens is {concave}.

Answer 1

Concept: The power of a lens is related to its focal length by the formula: \[ P = \frac{1}{f} \] where \(P\) = power of the lens (in dioptre) \(f\) = focal length (in meters)
Step 1:Substitute the given value.
Given power of the lens: \[ P = -2.0 \, D \] Using the formula: \[ f = \frac{1}{P} \] \[ f = \frac{1}{-2.0} \] \[ f = -0.5 \, m \]
Step 2:Convert into centimeters.
\[ f = -0.5\,m = -50\,cm \]
Step 3:Identify the type of lens.
Since the power and focal length are negative, the lens is a concave lens. \[ \boxed{f = -0.5\,m \; (or\; -50\,cm)} \]