# Reflection and Refraction of Light

Updated 01/2017 gmn, rc, jmh

__Materials__

1 each ray box

2 each multi-mirrors

1 each Lucite semi-circular lens

1 each rotating ray table

1 each metric ruler

graph paper (student-supplied)

__Goals__

1) To explore the reflection of a light ray from a shiny smooth surface.

2) To understand and observe how a curved mirror focuses incoming parallel light rays to a single point.

3) To explore the behavior of a light ray as it passes from one transparent medium into another transparent medium.

4) To verify that “Snell’s Law” of refraction holds for light rays passing from air to Lucite (a plastic) and from Lucite to air.

5) To calculate the “index of refraction” for Lucite from the data.

6) To observe the focusing of parallel rays of light by a semi-circular Lucite prism analogous to a simple lens.

__Introduction__

The basic behavior of light reflecting off mirror surfaces or passing from one medium to another is to be investigated. In our case, air and Lucite plastic are the two different media. A “ray box” produces one or more thin beams of light, rays if you will. Tracing the paths of these rays as they interact with a mirror or an interface graphically shows the behavior of light in these situations.

By convention the angle of incidence is defined as the angle between the incident ray and the normal (perpendicular direction) to the surface of the mirror or lens. When dealing with mirrors, the angle of reflection is the angle between the reflected ray and the normal to the surface of the mirror. When dealing with refraction, the angle of transmission is defined as the angle between the transmitted ray and the surface normal at that point.

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__Caution: Please avoid putting fingerprints on the surfaces of the optical elements. Handle them by the edges only.__

__Caution: Please avoid putting fingerprints on the surfaces of the optical elements. Handle them by the edges only.__

__Exercise 1: Reflection from a Plane Surface__

#### 1. By rotating the plastic mask on the front of the ray box, single or multiple rays can be obtained. Adjust it to give just one ray. The length of the ray box can also be adjusted to reduce spreading of the ray. Raise the ray box to the level of the rotating ray table (e.g. by placing it on the plastic lid of the optics kit). Use a rolled-up piece of paper tape to affix the rotating ray table to the lab table. Align the single ray of light so that it follows a path along the 0^{0}/360^{0} line through the center point of the ray table. Set the plane mirror side of one of the multi-mirrors at the center of the ray table aligned perpendicular to the ray of light. The incident and reflected light rays should be visible going through the “0” line of the rotating ray table to the mirror and reflecting back along the “0” line of the rotating ray table.

#### 2. Without changing the position of the mirror on the ray table, measure and record the angles of incidence and reflection (to the nearest 0.5°) as the incident angle of the ray is varied at 10^{0} increments from 10^{0} – 80^{0}. You will rotate the ray table to do this – the top of it rotates separately from the base (but you have to be gentle with it or you’ll displace your mirror). Make sure that the ray always strikes the mirror at the center of the ray table. Remember that incident and reflected angles are measured by convention from a line perpendicular to the mirror surface.

#### 3. Present your results in tabular form. From your data can you propose a general relationship between incident and reflected angles? How well is your hypothesis supported by the data? This is your chance for some error analysis. Assume 0.5° uncertainty.

__Exercise 2: Reflection from Two Plane Surfaces at Right Angles__

- The ray box remains the same as in Exercise 1. Using a piece of paper, place two plane mirrors (the straight sides of the multi-mirrors) at right angles to each other in an L-shaped formation on the paper.

- Now place the ray box so that the single ray impinges on the front of the mirror at its middle at an incident angle of about 45
^{0}. You should observe a reflected ray from this mirror combination. Use a ruler to draw on your paper the paths of both the incident and reflected rays. Now vary the incident angle of the incoming ray, always making sure that the ray’s path includes one reflection from each mirror surface, and again mark the paths of the incident and reflected rays from the mirror combination.

- Measure the separation (s) between each pair of lines at two points some distance (d) away from each other. Dividing the change in separation by the change in distance between the points measured yields the tangent of the angle ( tan(ϴ)=Δs/Δd ). Calculate this angle for each incident angle. From your observations what general rule might you suggest for the relationship between the incoming and outgoing rays for this configuration? How well does your data support your hypothesis (hint: what value should the angle be theoretically)?

An added note of interest:

Radar is another form of electromagnetic radiation, so exhibits the same properties as light when it comes to reflection. Radar often works by sending out a beam from a point, and then looking to see what, if anything, gets reflected back to that same point. An aircraft has many parts that fit together so that the surfaces make angles with each other. What angles should be avoided when designing “stealthy” aircraft, that is, those easy to “see” with radar?

__Exercise 3: Focal Length of a Concave Cylindrical Mirror__

- First, determine the radius of curvature of the mirror. Trace the edge of the mirror in pencil, then use a drawing compass (or pencil & string) to find the center of a circle that matches the curvature of the mirror. Measure the radius of this circle with a ruler. Estimate the uncertainty of this measurement (how much can you change the radius before noticing that it no longer matches the curvature of the mirror?). In theory, the focal length of the mirror should be half of the radius of curvature. Determine the theoretical focal length and its uncertainty.

- Adjust the ray box to give five parallel rays, and place a piece of graph paper in front of the ray box. Place the multi-mirror’s concave reflective surface toward the ray box with the center of the mirror surface perpendicular to the middle one of the five rays.

__Using pencil__, outline the position of the mirror on the paper. Then trace the path of each incident ray and its reflected ray.

- The “focal length” of the mirror is defined to be the distance from the center of the mirror to the point where parallel incident rays are caused to intersect after reflection from the surface. Determine the focal length for this concave mirror from your ray drawing. Compare the measured focal length with the theoretical prediction.

If all the rays don’t quite meet at a single point, this is called an “aberration.” Does this mirror exhibit any aberration? Does each of the five rays obey the simple rule of reflection from the mirror surface? Discuss and explain in each case.

__Exercise 4: Refraction (Semi-circular Lucite Piece)__

#### 1. Again select the single slit mask on the ray box, and align the incoming ray along the 0^{0}/360^{0} line through the center point of the rotating ray table. Place the flat face of the Lucite perpendicular to the direction of the ray. The rotating ray table has an outline of the Lucite semicircle to use as a guide. The ray of light should pass through the center of the flat side of the Lucite.

- Visually trace the path of the incoming ray from the ray box and the outgoing ray emanating from the curved side of the Lucite. Note that when the ray is perpendicular to the interface from air to Lucite or from Lucite to air, the ray does not deviate from its original direction. This means that the incident and refracted angles of the radial ray are both zero in this case. Now move the ray table so that the incident angle can be varied from 10
^{0}– 80^{0}in 10^{0}In each case record the angles of the incoming and outgoing rays.

**Note: It is imperative that the incoming ray strikes the Lucite at the center of the straight side of the semicircle each time. When that is the case the refracted ray at the straight side passes along a radius of the semicircle and will always strike the curved boundary of the Lucite at right angles (thus an incident angle of zero) so no additional refraction takes place. In other words, the angle measured on the curved side is the angle in the Lucite (****), and the angle measured on the flat side is the angle in air (****). Care here will ensure the validity of your data.**

- Historically the relationship between incident and refracted angles was not fully understood until the wave theory of light was proposed. It is now well understood and experimentally verified that light travels more slowly through a medium than through empty space. Air is mostly empty space so the slowing down of the light in air is very slight and can be ignored in many cases. The index of refraction of a material is defined as follows:

(index of refraction) n ≡ (light speed in vacuum) c/(light speed in mat’l) v

#### Consequently, the index of refraction for air is essentially 1.00 and that of the Lucite is greater than 1. Using a wave model it is predicted and verified by careful experiments that the correct relationship between the incident angle, θ_{i}, and refracted angle, θ_{r}, is:

n_{i }sin θ_{i} = n_{r} sin θ_{r} (This is called Snell’s Law)

where n_{i} is the index of refraction of the material for the incident ray and n_{r} is the index of refraction of the material for the refracted ray. *Now using Snell’s Law determine the index of refraction of the Lucite using graphical methods*. Hint: What is the slope of a graph of sin(θ_{Air}) vs sin(θ_{Lucite})?

- The behavior of the light traveling from air into Lucite is complete, but is the behavior of light traveling from Lucite into air the same? To explore this case put the ray box on the opposite side of the Lucite semicircle. Here the incoming ray should enter the Lucite through the curved boundary and pass along a radial line to the
*center*of the straight side. Here the ray leaves the Lucite and passes into the air. Again, measure incident (now in the Lucite) and refracted (now in the air) angles as before. Are there any differences that you discover? For fairly large incident angles what happens to the refracted ray? Record the “critical angle” where the refracted ray vanishes and only the reflected ray exists.**Don’t confuse the reflected ray with the refracted ray!**The effect that you are observing, called ‘total internal reflection’, is utilized in optical fiber transmission lines to keep the light from “leaking” out of the fiber. Determine the index of refraction of the Lucite from your data here in a similar way to that done in Step 3. Use Excel’s LINEST() function to determine uncertainty in your slopes. Do the values agree within the uncertainties?

__Exercise 5: Focal Length of a Lens (A Practical Application of Refraction)__

#### 1. Adjust the ray box to give five rays once again. Place the semi-circular prism (Lucite lens) on a piece of paper. Orient the lens so that the middle one of the five rays strikes the center of one side of the lens perpendicularly. Trace the incoming and outgoing rays. Does this lens have significant aberration?

#### 2. Rotate the lens by 180^{0} and trace the pattern of incoming and outgoing rays. Do they still converge? Try rotating the lens, say 20-30°. Does this change the focal length? Does this increase or decrease the aberration?