Explain Newton’s equation in the case of spherical mirrors
(qs mark 2)
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Formulae for spherical mirrors
For an object distance u, image distance v and focal length f we have:
1/u + 1/v = 1/f (Cartesian sign convention)
This formula applies to both convex and concave minors although you must remember to enter real distances as positive numbers and virtual distances as negative numbers.
Newton's formula:
Another useful formula is known as Newton's formula.
Let the distance of the object and image from the principal focus be x and y respectively.
Then
u= f+x and v= f+y
Using the mirror formula:
1/u + 1/v = 1/f gives
1/(f+x) + 1/(f+y) = 1/f and so:
Newton’s formula: f2 = xy
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