 ## Sunday, May 21, 2006

### Law of Reflection and Critical Angle

The Law of Reflection A = a’ where A = angle of incidence and a’ equals the angle of reflection. The angle of incidence and the angle of reflection are both measured from a normal to the surface. The normal is at 90° to the surface the light is hitting.

The Critical Angle occurs when going from a denser to a rarer medium. There is a point where a’ = 90° and all light is therefore internally reflected. The angle of incidence (a) that produces this condition is termed the Critical Angle (CA). Total internal reflection occurs when the angle exceeds CA. As n increases, CA decreases. The angle can be determined using Snell’s law as follows:

n sin ic = n’ sin 90° where: ic = the critical angle and the refracted angle is 90°,

sin ic = n’/n x 1

Question: What is the critical angle when going from water to air?

Answer: Use Snell’s law n (sin i c)= n’ (sin 90°)

ic = the critical angle

refracted angle is 90°

n = index of refraction for water = 1.33

n’ = index of refraction for air = 1.00

(sin ic) = n’/n x 1 = 1/1.33 = 48.75°

Question: What is the critical angle when going from a CR-39 (n = 1.4988) lens to air.

Answer: Use Snell’s law n (sin ic)= n’ (sin r)

i c= the critical angle

n = index of refraction of CR-39 = 1.4988

n’ = index of refraction of air = 1.00

r = 90°

sin ic = n’/n x sin 90° = 1/1.498 x 1 = 41.88°

Question: If light is passing through a prism and hits the second surface at the critical angle for the blue wavelength, red light will be:

a) totally internally reflected

b) will be refracted

c) this system is not subject to chromatic dispersion

Answer: b, Blue light has a smaller critical angle than red light because the refractive index of blue light is greater than the refractive index of red. As the refractive index increases, the critical angle decreases.

Question: What types of ophthalmic instruments are the applications of the critical angle the basis for?

Answer: Fiberoptics, gonioscopy, reflecting prisms, and Goldmann lens funduscopy. It is not related to retinoscopy.  