Optika
What you must know
Optika covers reflection, refraction (Snell's law n₁sin α₁ = n₂sin α₂), total internal reflection, lenses and mirrors (thin-lens equation 1/f = 1/a + 1/a′, magnification m = −a′/a), and wave optics: interference, diffraction and the spectrum. Know that light slows in a denser medium, that the critical angle satisfies sin α_c = n₂/n₁, and that a converging lens has positive focal length.
Traps
- Sign conventions for image distance and focal length; a virtual image has negative a′ for a lens.
- Forgetting that total internal reflection requires going from denser to less dense medium.
- Mixing up real and virtual images; a virtual image cannot be projected on a screen.
- Using degrees vs radians inconsistently in refraction problems.
- Confusing the focal length with the image distance.
Worked example
An object is 30 cm from a converging lens of focal length 10 cm. Find the image distance. Using 1/f = 1/a + 1/a′: 1/10 = 1/30 + 1/a′, so 1/a′ = 1/10 − 1/30 = 2/30, giving a′ = 15 cm. Magnification m = −15/30 = −0.5: the image is real, inverted and half-size. The negative sign confirms inversion.
Rule of thumb: light bends toward the normal when entering a denser medium. For lenses, sketch the three principal rays (parallel, through centre, through focus) to sanity-check your algebra.