The Newtonian Lens Equation
We have been using the “Gaussian Lens Formula”
1 1 1
+ =
p q f
An alternate lens formula is known as the Newtonian Lens Formula
x1 x2 = f 2
which can be easily verified by substituting p = f + x1 and q = f + x2 into the Gaussian Lens
Formula. Here, x1 and x2 are the distances to the object and image respectively from the focal
points. That is, x1 = (p-f) and x2 = (q-f) or q = f + x2 . (f is negative for a diverging lens).
Examples are attached.
Newtonian Lens Equation Examples:
1. An object is 15 cm from a converging lens which has a focal length of 10 cm, where is the
image?
x1 = (15 − 10) cm = 5 cm
f 2 100
x2 =
=
cm = 20 cm
x1
5
So the image is (10+20) cm = 30 cm to the right of the lens.
2. An object is 8 cm from a converging lens which has a focal length of 10 cm, where is the
image?
x1 = (8 − 10) cm = − 2 cm
f 2 100
x2 =
=
cm = − 50 cm
−2
x1
So the image is (10+(-50)) cm = -40 cm to the right, which is 40 cm to the left of the lens.
3. An object is 15 cm from a diverging lens which has a focal length of -10 cm, where is the
image?
x1 = (15 − ( − 10)) cm = 25 cm
f 2 100
x2 =
=
cm = 4 cm
x1
25
So the image is ((-10)+4) cm = -6 cm to right of lens, which is 6 cm to left of lens.