Refraction and Lens Power Worked Examples Cheat Sheet

Key Facts

• Refractive index is defined by $n = \frac{c}{v}$, where $c$ is the speed of light in vacuum and $v$ is the speed of light in the material.
• Snell's law is $n_1 \sin \theta_1 = n_2 \sin \theta_2$, where angles are measured from the normal line.
• When light enters a higher refractive index material, it bends toward the normal, so $\theta_2 < \theta_1$ if $n_2 > n_1$.
• When light enters a lower refractive index material, it bends away from the normal, so $\theta_2 > \theta_1$ if $n_2 < n_1$.
• The critical angle is found from $\sin \theta_c = \frac{n_2}{n_1}$ when light travels from a higher index medium into a lower index medium.
• Total internal reflection occurs only when $n_1 > n_2$ and the incident angle satisfies $\theta_1 > \theta_c$.
• Lens power is $P = \frac{1}{f}$, where $P$ is measured in diopters and focal length $f$ is measured in meters.
• A converging lens has positive focal length and positive power, while a diverging lens has negative focal length and negative power.

Vocabulary

Refraction

Refraction is the change in direction of light as it passes from one medium into another because its speed changes.

Refractive Index

Refractive index is a number that compares the speed of light in vacuum to the speed of light in a material using $n = \frac{c}{v}$.

Normal Line

The normal line is an imaginary line drawn perpendicular to the surface where the light ray meets the boundary.

Critical Angle

The critical angle is the incident angle that makes the refracted ray travel along the boundary at $90^\circ$.

Total Internal Reflection

Total internal reflection happens when light in a higher index medium reflects completely at a boundary with a lower index medium.

Lens Power

Lens power describes how strongly a lens bends light and is calculated using $P = \frac{1}{f}$ with $f$ in meters.