Answer to Question #285638 in Optics for NICKO

Question

Compare the mirror equation with the thin lens equation. Discuss similarities and differences, especially the sign conventions for the quantities involved.

Answer 1

the mirror equation is $\frac{1}{v}- \frac{1}{u}=\frac{1}{f}$ lens equation is $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ where $v=$ image distance u=object distance$f=$ focal length

Below applies to: Mirror and Thin Lens Equation: $\frac{1}{do}+\frac{1}{di}=\frac{1}{f}$

 Magnification Equation: Image height/Object height $=\frac{hi}{ho}=-\frac{di}{do}$

 Spherical Mirrors Lenses 

Focal Length (f)

+ for concave mirrors 

+ for a converging lens 

- for convex mirrors 

- for a diverging lens 

Object Distance (do) 

+ if object is in front of the mirror (real object)

+ if the object is to the left of the lens (real object) 

- if object is behind the mirror (virtual object)

 - if the object is to the right of the lens (virtual object)

Image Distance (di) 

+ if the image is in front of the mirror (real image)

+ for an image (real) formed to the right of the lens by a real object 

- if the image is behind the mirror (virtual image)

- for an image (virtual) formed to the left of the lens by a real object 

Magnification (m) 

+ for an image that is upright with respect to the object

+ for an image that is upright with respect to the object 

- for an image that is inverted with respect to the object

-for an image that is inverted with respect to the object. 

 Optical system that use multiple mirrors/lenses sometimes use the image formed by the first mirror/lens as the object for the second mirror/lens. When this happens, the object distance is negative and the object is said to be a virtual object.