Question Description

Need help with my Physics question - I’m studying for my class.

This is an online lab with online simulations and questions related to those simulations that needs to be answered. Please complete everything in the attached lab.

Objectives:

Upon successful completion of the laboratory exercise you will

• Veriy law of refraction
• Find index of refraction of an unknown material
• Create spectrum of light using prism
• Find criticle angle required for total internal reflection

Light

Reflection & Refraction

Critical Angle, Spectrum

Electricity and Light

This lab uses the Remote lab platform from PhET Interactive Simulations at University of Colorado Boulder, under the CC-BY 4.0 license.

This pre-lab is worth 5 points.

1. What does each term in equation [1] represent?

• What does the term Normal mean in the context of dealing with an optical surface?

• Describe how light behaves in relation to the Normal when travelling between two interfaces in the following cases:

From a less dense to a denser medium

From a denser to a less dense medium

• A convex lens is also known as a (converging, diverging ) lens and a concave lens is known as a  (converging, diverging) lens.

• Describe where the focal point for a convex and a concave lens located?

Objectives:

Upon successful completion of the laboratory exercise you will

1. Veriy law of refraction
2. Find index of refraction of an unknown material
3. Create spectrum of light using prism
4. Find criticle angle required for total internal reflection

Theory:

Whenever a wave traveling in some medium encounters an interface or boundary with another medium either (or both) of the processes of (1) reflection and (2) refraction may occur if the speed of the wave is different in the two media. 

If the wave being considered is light, the speed of light in any medium is characterized by the index of refraction for the medium, n, where

                                                                       n º c/v                                                               [1]

where c is the speed of light in a vacuum, and v is the speed of light in the medium. (Note that for a vacuum or air n=1.00.)

Reflection

In reflection, a ray of light traveling in a straight line in medium 1 encounters an interface with medium 2 and the incident ray is reflected (or bounced) backed into medium 1 at the interface of the two media as depicted in Figure 22 – 1.

		Figure 22 –1

The Normal is a reference line that is always perpendicular to the surface at the “point of impact” where the light is incident onto the surface. If the ray incident on the interface makes an angle q_I with the normal to the surface at the “point of impact” on the interface, the reflected ray will make an angle q_R with the normal from the “point of impact” equal to the incident angle q_I.  The relationship between the angles q_I and q_R for all reflections is called the Law of reflection which can be stated in two parts:

            1. q_I = q_R , and

            2. q_I  and q_R  are coplanar, (i.e. lie in the same plane.)                                   [2]

For light traveling parallel to the principal axis and is incident on a spherical (or cylindrical) surface with a radius R, the reflected light will cross the principal axis at a focal point, f, from the vertex (see Figure 22-2) such that

                                                                        f = R/2                                                               [3]

where R is the radius of curvature.

		Figure 22 –2

Refraction

In refraction, a ray of light traveling in a straight line in medium 1 encounters an interface with medium 2, penetrates the interface and then moves in a straight line in medium 2 as depicted in Figure 22 – 3.  If the incident ray originally in medium 1 makes an angle q₁ with the normal to the surface in medium 1, the refracted ray will make an angle q₂ with the same normal in medium 2.  The relationship between q₁ and q₂ for each refraction is called the law of refraction which can be stated in two parts:

            1. n₁ sin q₁ = n₂ sin q₂ , and                                                                              [4]

            2. q₁ and q₂ are coplanar.

		Figure 22 –3

Figure 22–3 represents two interfaces the first is from a lower to higher index of refraction (medium 1 (n₁) < medium 2 (n₂)), and the second is from a higher to low index of refraction (medium 2 (n₂) > medium 1 (n₁)).  At the interface of n₁ < n₂ the angle q₂ will be less than q₁ in relation to the normal which is in agreement with equation [4].  Likewise when n₂ > n₁ the angle q₃ will be greater than q₂ in relation to the normal.  From this it can be stated that:

A light ray incident at an angle q from the normal will bend towards the normal when traveling from a less dense medium to a denser medium, and bend away from the normal when traveling from a denser medium to a less dense medium.

Critical Angle

For any interface where light travels from a dense to less dense medium there can be found an angle of incidence from the normal which will cause the light ray not to penetrate the interface but to travel along the interface as shown in Figure 22-4.  Using Figure 22-3, it can be shown that if q₂ is increased from the normal, q₃ would eventually become 90° to the normal therefore the will travel along the surface of the interface.  The angle q₂ at this point is called the critical angle. From this it can be found that:

          [5]

In equation [5], (n₂/n₁) is called “the index of refraction of medium 2 relative to medium 1”. Note that if medium 2 is air then n₂ = 1 and that n₁ can be found by

                                                                   n₁ = 1/ sin q_c                                                           [6]

A phenomenon called total internal reflection occurs when the angle of incidence of the light ray from the normal at the dense to less dense interface exceeds the critical angle.  At all angles where q > q_c all of the light is reflected back into the denser medium.  Fiber optics is based upon this principal. 

Procedure:

PhET Simulation “Bending Light” at https://phet.colorado.edu/en/simulation/bending-light

Procedure: Part A Setup

1. Open the simulation “Bending Light” at PhET. Use the address above.
2. Click on Intro.
3. Leave the default for entry material at “Air”. Choose “Glass” for the exit material (See pic on right). Record the index of refraction of glass into Table 1
4. Choose the protractor and set the laser to an angle of incidence, θ₁, at 30°. Recall: angles are always measured from the Normal.
5. Ignore the reflected ray (the ray that remains in air). Using the protractor, measure the angle of refraction, θ₂, of the laser and record in Table 1.
6. Repeat steps 4 and 5 of this lab for 4 more angles of incidence of your own choosing. Record the results in Table 1.

Data:

Note* For best results center the protractor where the beam splits on the screen

Table 1

Trial	n1	θ1 (degrees)	θ2 (degrees)	Sin θ1	Sin θ2	nglass
1		30
2
3
4
5

Observations and Calculations:

1. Classify the bending of light as exhibited by the ray diagrams. According to your data, is light refracted away from or toward the normal as it passes at an angle into a medium with a higher index of refraction?

• Calculate sin θ₁ and sin θ₂ for each trial. Record the results in Table 1.
• Calculate n₂ (glass) for each trial. Record the results in Table 1.

• Compare the values for index of refraction of glass for each trial (values in last column). Is there good agreement between them? Would you conclude that index of refraction is a constant for a given medium?

• Compare your calculated n₂ with the given index of refraction, n_glass. Do they agree? Explain why it does or doesn’t.

Procedure: Part B Setup

1. Reset simulation and choose “Mystery A” for the material.
2. Choose the protractor and set the laser to an angle of incidence, θ₁, at 30°.
3. Ignore the reflected ray (the ray that remains in air). Using the protractor, measure the angle of refraction, θ₂, of the laser and record in Table 2.
4. Repeat steps 2 and 3 for angles of incidences of 40°,50°, 60°, and 70°. Record the results in Table 2.
5. Calculate sin θ₁ and sin θ₂ for each trial. Record the results in Table 2.

Table 2

Trial	θ1 (degrees)	θ2 (degrees)	Sin θ1	Sin θ2
1	30
2	40
3	50
4	60
5	70

• Draw a graph of the Sin θ₁ vs. Sin θ₂ on the grid below. Draw in your best-fit line and find the slope. Show slope work below. You can use excel and paste a screenshot of the graph if you like.

• What does your slope represent?

• Using the chart below of various indices of refraction for various media, identify your mystery material you had in your experiment.

• Find the percent error of your observed value (slope) using the identified index of refraction as your accepted value.

Analysis Questions:

1. Substitute the average value of the index of refraction that you measured in Part A into the equation for index of refraction and calculate the speed of light in the glass. Show work.

• What if you conducted this experiment (Part A) under water? Compare and contrast the results you get in such a situation to the results you have from this lab.

Now set up the materials as water on top and air on the bottom.

Move the laser back and forth

1. Somewhere between 30^o and 60^o the behaviour changes.

 What is the exact angle?

• What happens at this angle

Critical angle

When going from a more to a less dense material.

The light ray should be r________ away from the n_______

At the critical angle  the behaviour suddenly changes and the totality of all light is reflected back internally into the water.

This is called _________

Complete the table below (use air as the bottom material)

TOP Material	Refractive index (n)	critical angle ,θc /o	sin ,θc	1 / sin θc
Water	1.33	48	0.743	1.35
Glass
Mystery A

1. What effect does increasing the index of refraction have on the critical angle?

•  What equation can be used to calculate the critical angle

Spectrum

On the Prisms page of the simulation

phet.colorado.edu/sims/html/bending-light/

latest/bending-light_en.html

Select the white on black colour scheme

Set up the triangular block as shown.

Ensure the ray is pointed near the tip

Describe what you see.

à

Go to the More Tools page of the simulation

Use the spectrum to

investigate how color chages with wavelength

Complete the table

Wavelength nm	400	450	525	580	600	650	700
Color				Yellow

1. Describe the relationship between color and wavelength.

• Looking at the spectrum produced by the prism, which colour is bent more?

• Use this to explain which color slows down the most in a glass block

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