Digital Photography Part 1 A crash course in optics

Péter Tarján2 Light Photo + graphy (greek) = writing with light Light is an electromagnetic (EM) wave. EM waves are periodic changes in an electromagnetic field. Characteristics of light: speed of propagation:c (speed of light) wavelength:λ frequency:ν For any wave, speed of propagation equals the wavelength time frequency:

Péter Tarján3 The electromagnetic spectrum visible range 1 nm = m = 1 billionth of a meter = 1 millionth of a millimeter energ y

Péter Tarján4 Before we go on… Optics Geometric optics relatively easy Wave optics complicated deals with “rays” of light deals with wave equations

Péter Tarján5 Ray of light Ray of light/light ray: ideally, an infinitely thin beam of light Propagation: light ray travels in a straight line at speed c. The speed of light in vacuum is 300,000 km/s = 3×10 8 m/s – almost the same in air. Reflection: light ray is bounced back from a surface Refraction: light ray enters a different medium, wavelength and speed change Dispersion: on entering a dispersive medium, the components of light become spatially separated

Péter Tarján6 Dispersion White light consists of waves of various wavelengths (=different color). Separated components can be reunited with a lens, regaining white light. Some colors exist as both single-wavelength spectral colors and composite colors; some only exist as composite colors. A dispersive prism refracts light (changes its direction); resolves light into components of different color.

Péter Tarján7 Shadow Light sources in real life are never point-like and objects also scatter light, so shadows are never really black, not even full shadows, much less partial shadows. Shadows can be of any color, depending on the color of the light, the object and the surface!

Péter Tarján8 Rough surfaces Light incident on non-reflective, matte surfaces is scattered in every direction – that’s how we see objects from every angle. This phenomenon is called diffuse reflection. Not only surfaces scatter light. Seemingly transparent media, like air, also do – that’s why mountains in the distance seem hazy. But why is the sky blue and why are the clouds white? Research for yourself…

Péter Tarján9 Reflection Angle of incidence, angle of reflection are measured from the normal, not the surface. The Law of Reflection: the angle of reflection equals the angle of incidence: β = α. This type of reflection is called specular reflection.

Péter Tarján10 Plane mirror Image is upright virtual same size as object same distance behind mirror as object before it

Péter Tarján11 Spherical mirrors C: center of mirror V: vertex of mirror F: focal point CV line: optical axis CV distance: radius of the sphere FV distance: focal length = half the radius

Péter Tarján12 Principal rays

Péter Tarján13 Convex mirror aka diverging mirror Image is upright virtual reduced smaller distance behind mirror than object before it

Péter Tarján14 Concave mirror aka converging mirror

Péter Tarján15 Refraction When light enters a new medium, its direction, wavelength and speed changes. Wavelength and speed are highest in vacuum. Def.: index of refraction of a medium: n = c/v (v is speed in medium). Snell’s Law: (also called Descartes’ Law, Law of Refraction) consequences: mirage, different apparent size in water, etc. optically less dense medium optically more dense medium

Péter Tarján16 Total internal reflection Light moving from a dense to a less dense medium “bends away” from the normal; but the angle of reflection can be maximum 90 degrees (light is refracted along the surface). If the angle of incidence is increased beyond that critical angle, light is totally reflected rather than entering the new medium. light moves from a dense to a less dense medium

Péter Tarján17 Plane-parallel plate Light rays traveling through a plane- parallel plate (e.g. window glass) are shifted but their direction remains unchanged.

Péter Tarján18 Convex lens aka converging lens

Péter Tarján19 Concave lens aka diverging lens Image is upright virtual reduced closer to the lens than the object in front of the lens p

Péter Tarján20 d 0 is always positive d i is positive if image is behind the lens (real image) di is negative if image is in front of the lens (virtual image) f is positive for convex lens f is negative for concave lens d 0 : distance from object to center of lens d i : distance from image to center of lens f : focal length 1/f (f measured in m): power of the lens, measured in diopters. 1 D = 1/m Magnification of the lens: I : image size O : object size Thin lens equation

Péter Tarján21 Optical illusions The eye and the brain has the tendency not to see what’s actually there but what it thinks is there – this makes judging color, brightness and perspective especially difficult when taking photos…

Péter Tarján22 Imaging without lenses Possible! The camera obscura (Latin: dark room) or pinhole camera is a box with a little hole on one side. It creates a real, reversed image on the opposite side of the box. Image is less bright than with a lens, but depth of field is almost infinite – the smaller the hole, the more so. Needs long exposure, but free of distortion. Large creative potential!