Rays and Shadows

• Rays: In what circumstances we can assume that light travels along straight lines and casts sharp shadows beyond edges of extended objects, and why. What is geometric optics?
• Shadows: What are umbra and penumbra, how does one draw them; Be able to calculate their extent in specific situations; Their relation to the phenomenon of eclipses.

Reflection and Mirrors

• Reflection: Diffuse vs specular reflection; Use of the law of reflection, _i = _r, M = 1.
• Flat mirrors: Properties of the image; Use of geometry in problems with flat mirrors.
• Curved mirrors: Convex vs concave mirrors; parabolic vs spherical mirrors.
• Important concepts: Center, principal axis, vertex, focal point, focal length f = R/2 (including sign); Concept of aberrations in general and spherical aberration; Real vs virtual images.
• Mirror equation: The object and image positions are related by 1/s_o + 1/s_i = 1/f; each of the three quantities is positive if it refers to a location in front of the mirror, negative if behind.
• Magnification: By definition, m = h_i/h_o; Its value is equal to m = –s_i/s_o.
• Problem solving: Be able to apply both graphical method (ray tracing) and analytical method (mirror and magnification equations).

Refraction

• Refraction: Understand the general idea; The index of refraction of a transparent substance is n = c/v, where v is the speed of light in that material; it often depends on the wavelength.
• Snell's law: For light entering medium 2 from medium 1, n₁ sin ₁ = n₂ sin ₂.
• Total internal reflection: Occurs when n₂ < n₁ and the angle of incidence is larger than the critical angle _c satisfying sin _c = n₂/n₁.