Spherical Mirrors Rules & Regulations

Rules for signs for spherical mirrors

Front side of mirror	Back side of the mirror
Incident Light Reflected Light f & R positive object and image distances positive M > 0 means erect image M < 0 means inverted image	no light f & R negative object and image distances negative

Mirror Equation:

s = distance from object to mirror

s' = distance from image to mirror

R = radius of curvature of mirror

f = focal length of mirror

Conventions for Refracted light

Light side / incident light side	Back side / refracted light side
Incident Light object distance positive s > 0 image distance negative s' < 0 Radius of curvature negative R < 0 Focal length negative f < 0	refracted Light object distance negative s' < 0 image distance positive s > 0 Radius of curvature positive R > 0 Focal length positive f > 0

Refracted Image equation

, where

n₁ = index of refraction for the incident light side

n₂ = index of refraction for the refracted side

s = distance from object to the interface

s' = distance from image to interface

R = radius of curvature NOTE:for flat surfaces, R = ∞

Thin Lenses:

Assumptions:

Thickness is small enough to be ignored

Distance between lite rays and Principle Axis are small compared to R₁ and R₂ (so u ≈ sin u ≈ tan u)

Biconvex = converging = positive lens for which f > 0

Biconcave = diverging = negative lens for which f < 0

For lite rays going from air to lens to air the lens equation is :

NOTE: for converging lens R₁ > 0 and R₂ < 0

and for diverging lens R₁ < 0 and R₂ > 0

M > 0 means erect image and on same side as object (virtual image) incident lite side

M < 0 means inverted image and on opposite side as object. dark side

Ray diagrams: Use two rays from top of object