Optics
What the exam tests
Optics covers vergence, lens power, image formation, refractive index and prisms. Questions often ask you to calculate a focal length, apply the thin-lens formula or state the direction of prism deviation.
Lens power and vergence
Power in dioptres is D = 1/f, where f is the focal length in metres. Converging lenses are positive; diverging lenses are negative. Vergence L = 1/l in metres in air. For a thin lens, object vergence plus lens power equals image vergence: U + P = V. The eye has total power of about 60 D, of which the cornea contributes about 43 D. Refractive indices: cornea 1.376, aqueous and vitreous 1.336, crystalline lens about 1.42. Snell's law, n1 sin i = n2 sin r, explains refraction at each surface.
Prisms
A prism deviates light toward its base and is labelled in prism dioptres. One prism dioptre deviates a ray by 1 cm at 1 m. Prentice's rule is P = cF, with c in centimetres and F in dioptres.
Worked example
A +4.00 D lens is held 25 cm from an object. Object vergence U = 1/(−0.25) = −4.00 D. Then V = U + P = −4.00 + 4.00 = 0, so the image is at infinity. If the object were at 50 cm, U = −2.00 D and V = +2.00 D, giving an image 0.5 m beyond the lens.
Traps
Watch signs: a diverging lens has negative power and a virtual image. Do not use millimetres in Prentice's rule. Prism base direction is opposite to the apparent image shift, and axis notation is not a prism direction.