# Power of a spherical refracting surface

The power of a spherical refracting surface is given as, P = (n2 – n1)/R
Where n1 = refractive index of object space, n2 = refractive index of image space
R = Radius of curvature of the spherical surface
I tried to derive the expression but I got a different expression.
Let u and v be the object and image distance from the spherical surface respectively.
Suppose the spherical refracting surface produces the image of a real object placed at its first principal focus at infinity. Then,
u = +f1, v = infinity
For refraction at a spherical surface,
(n2)/v + (n1)/u = (n2 – n1)/R
(n2)/(infinity) + (n1)/f1 = (n2 – n1)/R
0 + (n1)/f1 = (n2 – n1)/R
f1 = [(n1)(R)]/( (n2 – n1)
Power = 1/f1
Therefore P = (n2 – n1)/[(n1)(R)]
Could you please tell me where I have gone wrong?

## Answers and Replies

Andrew Mason
Homework Helper
Amith2006 said:
The power of a spherical refracting surface is given as, P = (n2 – n1)/R
Where n1 = refractive index of object space, n2 = refractive index of image space
R = Radius of curvature of the spherical surface
I tried to derive the expression but I got a different expression.
Let u and v be the object and image distance from the spherical surface respectively.
Suppose the spherical refracting surface produces the image of a real object placed at its first principal focus at infinity. Then,
u = +f1, v = infinity
For refraction at a spherical surface,
(n2)/v + (n1)/u = (n2 – n1)/R
(n2)/(infinity) + (n1)/f1 = (n2 – n1)/R
0 + (n1)/f1 = (n2 – n1)/R
f1 = [(n1)(R)]/( (n2 – n1)
Power = 1/f1
Therefore P = (n2 – n1)/[(n1)(R)]
Could you please tell me where I have gone wrong?
It looks like f1 is the focal length in air (n = 1). The power is the reciprocal of the focal length in the medium. That focal length is f1/n1 in a medium with index of refraction n1. So the power is P = n1/f1

AM