# PHYS 402 Introduction to Ray Optics and Percent Difference Lab Report: Physics Answers 2021

PHYS 402 Introduction to Ray Optics and Percent Difference Lab Report: Physics Answers 2021

## PHYS 402 Introduction to Ray Optics and Percent Difference Lab Report: Physics Answers 2021

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PHYS 402 Introduction to Ray Optics and Percent Difference Lab Report

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April 5, 2021
Introduction to Ray Optics
In this lab, you will investigate ray optics and the reflection and refraction
of light rays.
When the wavelength λ of light is small compared to the relevant size (d)
of the object that it interacts with, then the wavelike properties of light such
as diffraction and interference can usually be ignored. Since the wavelength
of visible light falls in the range of approximately 350 nm ≤ λ ≤ 750 nm, it is
usually safe to neglect these effects and treat light as propagating in straight
geometrical lines, or rays.
In this model of light propagation, light reflections behave as:
θr = θi
(1)
which simply states that the angle of reflection of a light ray is equal to the
angle of incidence. Note that both angles are measured with respect to the
normal to the surface.
Light rays will also refract, or bend, as they pass from one medium to
another as shown in Fig. 1. Snell’s law dictates that the angle of incidence
θ1 and the angle of refraction θ2 are related by:
n1 sin θ1 = n2 sin θ2
(2)
where n is the index of refraction, and is characteristic of each material. n
is defined as
n=
c
v
(3)
where v is the speed of light in the material, and c = 3 × 108 m/s is the speed
of light in vacuum. Note that n is always greater than or equal to 1, so the
speed of light in any material is always less than c = 3 × 108 m/s.
When passing from a denser medium to a less dense medium –such as
from water into air– n1 is greater than n2 , and the angle of the refracted
ray bends away from the normal. There is a ‘critical’ incident angle θC for
which the refracted ray angle is 90◦ and the light ray skims along the surface.
Figure 1: Reflection and refraction of a light ray at an interface between two
mediums.
Figure 2: Total internal reflection of a light ray at an interface between two
mediums.
n1
θ1
1.00
1.00
1.33
1.33
34
70
34
70
I
v1
reflected
n2
θ2
θ2
I
v2
v2 Iref lect +Iref ract
obs calc refracted obs calc
1.33
1.33
1.00
1.00
x
x
x
x
Table 1: Format for tabulating your observations. In this table, the subscript
1 refers to the incident beam and the subscript 2 refers to the refracted beam.
‘x’ indicates places you do not need to provide any value.
For all incident rays with angles larger than the critical angle, no light will
escape the first medium, and all light undergoes ‘Total Internal Reflection’,
as shown in Fig. 2. It’s easy to show, by just inserting 90◦ for θ2 into Eq. 2
that

−1 n2
(4)
θcrit = sin
n1
Instructions
Now let’s get to the lab. Prepare a table like Table 1 in which you will record
Choose the More Tools panel to work in.
1
Reflection and Refraction (60pts)
Select Ray, and turn on Normal. The upper material should be Air and
the lower material should be Water. Click the red laser button to turn it on.
Activate a protractor by dragging it out of the toolbox. Activate a velocity
meter and an intensity meter by dragging them out of the toolbox.
Measure the angle of reflection with the protractor and verify that it is
what you would expect.
1. Set the incident angle to a value of θ1 in Table 1. Also set the indexes of
refraction of the two materials to match what is in this row of Table 1.
2. Calculate what the expected angle of refraction will be and enter it into
Table 1.
3. Use the protractor to measure the angle of refraction. Enter your observed values in Table 1.
4. Use Eq. 2 to calculate what the angle of refraction should be and enter
that value in Table 1.
5. Use Eq. 3 to calculate what the velocity of the light should be for the
refracted ray, then drag the velocity meter on to the desktop and use
it to measure the speed. Enter your results in Table 1.
6. Use the intensity meter to measure the intensity of the reflected ray
and the refracted ray. Enter these values and their sum in Table 1.
7. Repeat for all rows of Table 1.
The writeup for this section is Table 1, along with a short discussion of
the following questions.
• Compare the values you get for θ2 calculated vs θ2 measured by taking
the percent difference:
|θ2calculated − θ2measured |
× 100
θ2calculated
(5)
Discuss any large discrepencies.
• Compare the values you get for v2 calculated vs v2 measured by taking
the percent difference:
|v2calculated − v2measured |
× 100
v2calculated
(6)
Discuss any large discrepencies.
• What do you find for the sum of refracted and reflected ntensities?
What do you expect to find for this sum?
n1
n2
θc
θc
observed calculated
1.33 1.00
1.50 1.00
1.60 1.33
Table 2: Format for tabulating your observations. In this table, the subscript
1 refers to the incident beam and the subscript 1 refers to the refracted beam.
2
Total Internal Reflection (40 pts)
In the previous section, you will have observed that there was a situation
where the incident beam was totally internally reflected and no beam emerged
into the second medium. We will investigate this further in this section.
Prepare a table like Table 2 in which you will record your observations
1. Select a row in Table 2, and enter those values for n1 , n2 into the
simulation .
observe that there is no refracted ray. Enter this value into table 2.
3. Calculate what the critical angle should be for this interaction and
enter it into table 2.
4. Repeat for all rows of Table 2.
The writeup for this section is Table 2, along with a short discussion of
the following questions.
• Compare the values you get for θc calculated vs θc measured by taking
the percent difference:
|θccalculated − θcmeasured |
× 100
θccalculated
(7)
Discuss any large discrepencies.
• What constraint on the values of n1 and n2 is necessary for there to be
Total Internal Reflection?

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