Following formula is known as “Gaussian Lens Formula”
1/O+1/I=1/f
where O is object distance, I is image distance and f focal length of lens.
An alternate lens formula is known as the Newtonian Lens Formula
which can be obtained by substituting O = f + x and I = f + y into the Gaussian Lens Formula. Here, x and y are the distances of the object and image respectively from the focal points. We get
1/(f + x)+1/( f + y)=1/f
=>((f+y)+(f+x))/((f + x)( f + y))=1/f
After simplifying and Cross-multiplying we get
f(2f+x+y)=(f + x)( f + y)
=>2f^2+xf+yf=f^2 + xf+ fy + xy
=>f^2= xy
(In calculations f is taken as negative for a diverging "concave" lens).
-.-.-.-.-.-.-.-.-.-.-.
Example
Q. An object is located at 15 cm from a diverging lens which has a focal length of -10 cm. Where is the image formed?
A.
By definition of x
x=O-f
=>x=15-(-10)=25cm
Using the formula
f^2=xy
=>y=f^2/x=(-10)^2/25=4cm
Now the image distance I=f+y
=>I= (-10)+4 = -6 cm to right of lens, which is 6 cm to left of lens.
