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The power of a lens is -2.5 D. What is its focal length?
40 cm
+40 cm
25 cm
+25 cm
40 cm
The power of a lens is defined as the reciprocal of its focal length in meters. Given the power P=тИТ2.5┬аD, the focal length f is calculated as f=P1тАЛ, resulting in тИТ0.4┬аm, which converts to тИТ40┬аcm.
The power of a lens is defined as the reciprocal of its focal length in meters. Given the power P=тИТ2.5┬аD, the focal length f is calculated as f=P1тАЛ, resulting in тИТ0.4┬аm, which converts to тИТ40┬аcm.
Think of a diverging lens like a wide-angle door peephole that spreads light out to help you see a larger area; because the rays move away from each other, the 'focus' is mathematically behind the lens, giving it a negative value.
P-F-M: Power is inverse of Focal length in Meters.
P=f(m)1тАЛ тАФ Power in Diopters equals reciprocal of focal length in meters
f(cm)=P(D)100тАЛ тАФ Conversion formula when focal length is required in centimeters
Lens power measures the ability of a lens to converge or diverge light rays. A negative power indicates a concave (diverging) lens, which by sign convention has a negative focal length. The relationship between power and focal length is governed by the formula P=f(in┬аmeters)1тАЛ.
Diopter (D) is the SI unit of power, equivalent to mтИТ1.
Concave lenses always have negative power and focal length.
Convex lenses always have positive power and focal length.
The sign convention is essential for determining lens type in optical problems.
Diopters provide a simple additive value for combined lenses in series: PtotalтАЛ=P1тАЛ+P2тАЛ+...
The power model assumes thin lenses and paraxial rays; it fails for thick lenses or wide-angle aberration analysis.
Prescription glasses for myopia (nearsightedness) use concave lenses with negative power.
Calculating the combined refractive effect of multiple lenses in optical instruments.
Standard unit for Power is Diopter (D).
Option B (+40 cm) would be the answer for a convex lens of +2.5 D power.
Option C (-25 cm) corresponds to a power of -4 D.
A is correct тАФ The focal length is the reciprocal of the power, and for a power of -2.5 D, the focal length is -0.4 m, which is -40 cm.
Always ensure your focal length units match the power unit requirements; if focal length is in cm, use P=f100тАЛ.