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Worksheet 11: Optics – Reflection, Refraction, and Lenses

Introduction

In this lab, you will explore fundamental principles of geometrical optics, including the behavior of light as it reflects, refracts, and passes through lenses. The lab includes direct observation and measurement of phenomena such as reflection, refraction, total internal reflection, image formation by mirrors and lenses, and dispersion through a prism. These topics are essential to understanding the behavior of light in both everyday optical devices and scientific instruments.

Key Concepts

Law of Reflection

The Law of Reflection states that the angle of incidence \theta_i equals the angle of reflection \theta_r :

\theta_i = \theta_r

Refraction and Snell’s Law

When light passes from one medium to another, it bends according to Snell’s Law:

n_1 \sin \theta_1 = n_2 \sin \theta_2

Where n is the index of refraction. Total internal reflection occurs when light attempts to move from a higher-index to a lower-index medium and exceeds the critical angle:

\sin \theta_c = \frac{n_2}{n_1}

Mirrors and Lenses

For both spherical mirrors and thin lenses, light rays obey predictable rules of image formation:

  • Mirror equation and thin lens equation:
\frac{1}{p} + \frac{1}{i} = \frac{1}{f}

Where p is object distance, i is image distance, and f is focal length. For spherical mirrors, f = R/2 , where R is the radius of curvature.

  • The Lensmaker’s Equation for a lens in air:
\frac{1}{f} = (n - 1)\left( \frac{1}{R_1} - \frac{1}{R_2} \right)

Dispersion

Light of different wavelengths refracts at different angles, with shorter wavelengths (e.g., violet) bending more than longer ones (e.g., red). This separation of colors by wavelength is called dispersion and is most commonly observed with a prism.

Overview of Measurements

Measurement 1: Law of Reflection

  • Using a plane mirror and ray table, you measure the angle of incidence and corresponding angle of reflection across a range of angles.
  • Results are used to confirm the Law of Reflection.
Figure 1: Measurement 1 set-up
A single ray hitting the plane mirror

Measurement 2: Law of Refraction and Total Internal Reflection

  • A D-shaped lens is used to measure refraction through the flat surface.
  • You collect data to apply Snell’s Law and identify the critical angle.
  • Beyond the critical angle, you should observe total internal reflection.
Figure 2: Measurement 2 set-up
A single ray hitting the D-shaped lens
Figure 3: Example of refraction
This is an example of what you will see when conducting this measurement. You may notice, as shown in this figure, that you may see 3 light rays in total: the incident ray, the refracted ray, and then a fainter, thin ray. Do not pay attention to the faint thin ray, you want to look at the brighter refracted ray when collecting your data.

Measurement 3: Focal Lengths of Spherical Mirrors

  • Both concave and convex mirrors are investigated using parallel rays.
  • You determine the focal point and radius of curvature using ray tracing and direct measurement.
  • Virtual focal points are found for convex mirrors by back-tracing diverging rays.
Figure 4: Measurement 3 set-up with concave mirror
This is the set-up with the 5 light-ray settings (the 3 light-ray setting will be exactly the same). Notice where the rays converge and how a point was marked. This is the focal point.
Figure 5: Measurement 3: Concave mirror: example results
Figure 6: Measurement 3 set-up with convex mirror
This is the set-up with the 5 light-ray settings (the 3 light-ray setting will be exactly the same). Notice how the rays begin diverging,but seem to converge behind the convex mirror. You will need to use ray-tracing to find the focal point behind the mirror.

Measurement 4: Focal Lengths of Thin Lenses

  • Both convex (converging) and concave (diverging) lenses are studied.
  • You use ray tracing with parallel rays to identify and measure real and virtual focal points.
Figure 7: Measurement 4 set-up with convex lens
Figure 8: Measurement 4 set-up with concave lens

Measurement 5: Hollow Lens Filled with Water

  • The hollow lens behaves like a plano-convex lens when filled with water.
  • You observe focusing behavior and calculate the focal length using the lensmaker’s equation.
Figure 9: Measurement 5 set-up with hollow lens

Measurement 6: Dispersion with a Prism

  • White light is passed through a prism to observe dispersion.
  • You identify which colors deviate most and least, linking this to how the index of refraction varies with wavelength.
Figure 10: Measurement 6 set-up with prism

Objectives

By the end of this lab, you will be able to: - Confirm the Law of Reflection using experimental data. - Apply Snell’s Law to measure indices of refraction and observe total internal reflection. - Determine focal lengths and radii of curvature for spherical mirrors and thin lenses. - Use the lensmaker’s equation to relate lens geometry and refractive index to optical power. - Observe and explain the phenomenon of dispersion in a prism. - Understand and apply appropriate sign conventions and ray tracing techniques in optics.

Materials List

  • Ray Optics Kit (including plane mirror, D-shaped lens, convex/concave mirrors, lenses, prism)
  • Ray Table
  • Light Source (with single, 3-ray, and 5-ray modes)
  • White Paper and Ruler
  • Water and Hollow Lens
  • Datasheets or Manual (for radii of curvature and nominal focal lengths)