Geometrical Optic
Reflection on Plane Mirror
Image Formation In Plane Mirror
Image of a point object
Image properties
Image is virtual (no actual rays intersect to build the image)
Image cannot be projected on a screen.
Image distance = object distance
Image of an extended object on a plane mirror. All the properties are the same as that of
the point object
Image Properties
Transverse orientation of image and object are the same
A right‐handed object has a left‐handed image
Image size = object size or magnification = 1
Image location does not depend on the observer
The mirror does not lie directly below the object where the mirror can be extend to construct the
image.
Multiple images of a point object from direct reflections and multiply reflected light rays
Refraction through plane surfaces
Extension of the rays emerging from point object S do not converge to an image point
Using the paraxial optics approximation i.e. working with the rays that remain close to the central axis i.e. sin θ ≈ tan θ≈ θ ≈60 ≈ 0.1 radians, we can observe an image of S at S’
From Snell's law for paraxial rays :
n1 tan θ1 = n2 tan θ2 analogous to n1(x/s) = n2 (x/s')
Location of the image point: s' = (n2/n1) s
If n2 < n1 then s ' < s and the image forms above the object point.Apparent depth is smaller
than the reality (looking into water)
If n2> n1 then s ' > s and the image forms below the object point. Apparent depth is larger
than the reality (seeing objects from a pool)
Specular reflection
Reflection at a spherical surface : first order approximation (paraxial)
A relationship between s and s' that only depends on R. draw two rays one hits the
vertex, and the other one hits an arbitrary point on the optical system. Using the law of
reflection, the two rays hitting V and P can be traced.
From the figure we can write:θ=α + Φ; 2θ = α + α
The relationship has to be independent of the ray we choose to trace so we have to eliminate
θ between the two equations:
α - α' = -2 Φ
Diffuse reflection
From a granular surface :
though the law of reflection is obeyed for each ray
locally microscopically granular surface results in diffusing the beam.
From a perfectly smooth surface:
all of the rays from a parallel incident
beam reflect as a parallel beam.
Corner Cube Reflector
Reflects the outgoing rays exactly parallel to the
incoming rays regardless of incidence angle
