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Convergence lens focal length and power

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Shows a sketch of the lens with the surface labeled in reference to their curvature as seen from the left side, assume to be the side of the incident light.
a) Find the focal length of this lens?
b) Find optical power of the lens?
 
Optics - Convergence lens focal length and power Optics - Convergence lens focal length and power - Physics Problems
Below diagram shows a sketch of the lens with the surface labeled in reference to their curvature as seen from the left side, assume to be the side of the incident light. The lens is made out of glass (index of refraction n = 1.5).
a) Find the focal length of this lens?
b) Find optical power of the lens?
 
Convergence lens
Convergence lens

Using lensmaker’s equation
lensmaker’s equation

Following the sign convention for spherical refracting surfaces, we have

Convex: R1 = + 8 cm
Concave: R2 = - 8 cm

Using these values for radii and n = 1.5 for the index of refraction, we can find focal length for this lens
lensmaker’s equation
focal length
focal length

f = 8 cm

Focal length of the lens is 8 cm.

Notice that f = R1. One can show that this simple relationship holds for any symmetric lens made of glass with index of refraction n = 1.5.

The optical power P of a lens is defined as the inverse of its focal length.
optical power
optical power
optical power
optical power
P = 12.5 d

Optical power of the lens is 12.5 d.
 
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