Find the focal length of a lens of power – 2.0 D. What type of lens is this?
Given: Power of the lens, P = – 2.0 D.
We know that the power of a lens is the reciprocal of its focal length. The formula is: P = 1/f
To find the focal length, we rearrange the formula: f = 1/P
Substituting the given value of power: f = 1 / (– 2.0) f = – 0.50 m
Thus, the focal length of the lens is – 0.50 m.
Regarding the type of lens, the provided text states that the power of a convex lens is positive and that of a concave lens is negative. Since the given power is negative (– 2.0 D), this is a concave lens.
Explanation
The solution is derived directly from the section '9.3.8 Power of a Lens' in the provided text. The formula P = 1/f is used to calculate focal length. The text explicitly states that '1 dioptre is the power of a lens whose focal length is 1 metre', establishing the unit conversion. Furthermore, the context clarifies the nature of the lens by stating, 'the power of a convex lens is positive and that of a concave lens is negative,' which allows us to identify the lens with negative power as concave.
Solution Steps
Step 1: Identify the given value: Power P = – 2.0 D.
Step 2: State the relation between power and focal length from the text: P = 1/f.
Step 3: Rearrange the formula to find focal length: f = 1/P.
Step 4: Calculate the focal length: f = 1 / (– 2.0) = – 0.50 m.
Step 5: Identify the lens type based on the sign of power: Since power is negative, the lens is concave.