Optics: Mirrors & Lenses

Plane Mirrors
• Law of Reflection
• Object distance, image distance
• Where do images form?
• Where light rays actually meet (converge) OR where they APPEAR to originate (diverge from a certain point)
• Real image, virtual image

Plane Mirrors

Magnification
• In plane mirrors, objects do not appear larger or smaller than normal (this will change for curved mirrors)
• h o
= object height, h i
= image height
• s o
= object distance, s i
= image distance

Curved Mirrors
• Concave, Convex
• Spherical mirrors
• Center/radius of curvature, principal axis

Curved Mirrors f = R/2

Concave Mirror Ray Diagrams
• Ray parallel to the principal axis reflects through the focal point on the object side of the mirror
• Ray that hits the vertex reflects across the principal axis following the Law of Reflection
• Ray that goes through the focal point (or is lined up with the focal point) on the object side of the mirror reflects parallel to the principal axis
• Ray that goes through the center of curvature is reflected back on itself

Concave Mirror Ray Diagrams

Convex Mirror Ray Diagrams
• Same rules as concave EXCEPT….
• Use the focal point that is on the OPPOSITE side of the mirror as the object

Sign Conventions for Mirrors
• s o
, s i
, f are all POSITIVE if they are in front of the mirror’s reflective surface (NEGATIVE if behind)
• h i
is POSITIVE if the image is upright,
NEGATIVE if it is inverted

Thin Lenses
• Refract light rays to form images
• Converging, diverging lenses
• Light bends at each glass/air boundary, but common to show change in direction at center of lens
• f is positive for converging lenses, negative for diverging lenses

Converging Lens Ray Rules
• Ray parallel to the principal axis refracts through the focal point on the object side of the lens
• Ray that goes through the focal point (or is lined up with the focal point) in front of the lens refracts parallel to the principal axis
• Ray that goes through the absolute center of lens continues in a straight line

Converging Lens Diagrams

Diverging Lens Ray Rules
• Same as converging rules EXCEPT…
• Ray parallel to the principal axis refracts lined up with the focal point in front of the lens
• Ray that “goes through the focal point” actually just aims towards focal point behind the lens (then comes out parallel)

Diverging Lens Ray Diagrams

Thin Lens Equations
• GOOD NEWS!!!
• SAME magnification equation applies to thin lenses!!!
• The equation below that applied to mirrors also applies to lenses!!!

Sign Conventions for Thin Lenses
• s o is POSITIVE if the object is in front of the lens (side from which light approaches),
NEGATIVE if the object is behind the lens
• s i
is POSITIVE if the image forms behind the lens, NEGATIVE if the image forms in front of the lens

Thin Lens Characteristics
• Focal length of a lens is related to two things:
– the curvatures of its front and back surfaces
– the index of refraction of the lens material
• Generally, the “thicker” the lens, the shorter its focal length
• Greater index of refraction, shorter focal length

Multiple Lenses
• M total
= (M
1
) (M
2
) (M
3
)…
• Use image of first lens as object for next lens