L.1- Thick Prisms

Optometry and Prism Optics

Introduction to Prisms

• A prism is a piece of glass with flat surfaces, contrasting with lenses that have curved surfaces.

• The flat surfaces of the prism have no dioptic power; they do not affect the vergence of light passing through.

• Prisms are boundaries between two media (e.g., air and glass).

Dioptic Power of Prisms

• A flat surface has an infinitely long radius of curvature, leading to:
  $\text{Power (P)} = \frac{n<em>2 - n</em>1}{r}$
  Where:

  • $n_1$: index of the first medium (e.g., air)

  • $n_2$: index of the prism material (e.g., glass)

  • $r$: radius of curvature

• For flat surfaces, since $r \to \infty$, then
  $P = 0$
  Thus, prisms do not change the vergence of light:

  • Light remains diverging if it was diverging before it entered the prism.

  • Light remains parallel if it was parallel before entering the prism.

Refraction and Snell's Law

• Light bends at interfaces due to Snell's Law: $n<em>1 \sin(i</em>1) = n<em>2 \sin(i</em>2)$ Where:

  • $i_1$: angle of incidence

  • $i_2$: angle of refraction

• Light travels from air into glass (high index) -> bends toward the normal, vice versa for glass to air (low index).

Flat Slabs vs. Prisms

• A flat slab is a rectangular prism with parallel surfaces:

  • Light bends upon entering and exiting but exits parallel to its entry path (lateral parallel displacement).

  • No change in vergence, hence, clear images from behind the slab.

• A triangular prism:

  • Has angled surfaces, thus changes the direction of light.

  • Light deviates toward the base of the prism while the image shifts toward the apex.

Image Perception through Prisms

• When observing through a prism:

  1. Light enters the prism, bends toward the base.

  2. Light exits and shifts the perceived image location.

  3. The image appears switched towards the apex of the prism.

  4. This shift causes the perception of objects to move from their true position.

• Key points:

  • No change in clarity (virtual images, same size as objects).

  • $u + d = v$ where:

  • $u$: object distance (diverging light)

  • $d$: distance (zero for prisms)

  • $v$: image distance (equal to $-u$ thus virtual).

Deviation Angle

• Defined as the angle between the original path of the light and the new path post refraction: $\delta = i<em>1 + i</em>2' - \alpha$ Where:

  • $\delta$: deviation angle

  • $i_1$: angle of incidence at the front surface

  • $i_2'$: angle of light as it exits

  • $\alpha$: apex angle of the prism.

Calculating Deviation Angles

• Light transitioning through a prism has several angles to consider for calculation:

  1. For the First Surface: Use Snell's law to obtain $i_1'$ (angle after refraction).

  2. For the Middle of the Prism: Use the formula to calculate the next angle $i_2$.

  3. For the Second Surface: Apply Snell's law again for $i_2'$ (angle as it refraction leaves the prism).

Examples

• Example 1: Prism with apex angle of 50° and index of 1.617

  • Incoming ray at 70°. Find total deviation (d). Calculations lead to:
    $\delta = i<em>1 + i</em>2' - \alpha = 70 + 23.8 - 50 = 43.8°$

• Example 2: Prism with apex angle of 30° at a 45° incoming ray leads to a unique deviation value calculated through similar steps as above.

Prism Diopters and Deviation Angles

• Relationship:

  • $\Delta = \frac{100 \tan(\delta)}{1}$
    Where:

  • $\Delta$: prismatic power (in prism diopters)

  • $\delta$: deviation angle (in degrees)

  • A 5 diopter prism implies a specific angle deviation proportional to light bending.

Corrective Applications of Prisms

• Important for measuring ocular alignment:

  • Moving image positions into the aligned visual field of the affected eye.

• Uses of Base Indications:

  • Base in for exotropic alignments (right eye deviating outwards)

  • Base out for an estramus with inward deviations.

• Prisms also help more effectively measure visual field deficits, moving the visual field into the perceived area that may otherwise be lost.

Conclusion

• Understanding prism function in optics is vital for both corrective and diagnostic applications in optometry.

• Prisms manage the direction of light, assisting in daily vision corrections.