Physics lab

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LAB#3: REFRACTION AND LENSES

OBJECTIVES

• Understand Snell’s law of refraction

• Understand what convex and concave lenses are and how they refract light by utilizing Snell’s Law

• Learn how the focal length (f), object distance (do), and image distance (di) are related for a thin lens

WRITEUP REQUIREMENTS

Informal: Questions – 6 pts, Data Tables – 4 pts

PART 1: REFRACTION

PREPARATION

Refraction refers to light bending as it moves from one medium (material) to another. The bending of light depends

on a material property known as the index of refraction, n (note n is a unitless quantity). Materials used for optics

will typically have an index of refraction somewhere between 1.0 and 2.0. How a light ray bends when it is refracted

will also depend on the incident angle. The incident angle is measured with respect to the surface normal.) This is

described mathematically by Snell’s Law, which is given by

𝑛𝑖 sin(𝜃𝑖 ) = 𝑛𝑟 sin(𝜃𝑟 ) (3-1)

Some general results from Snell’s law that are worth noting is how light bends when it moves from one medium to

one with a lower, higher, or identical index of refraction. When moving to a lower index material, the light will bend

farther away from the normal. Conversely, light bends closer to the normal when the light moves into a higher

index. Then there will be no bending when the two materials have the same index. (See Figure 3-1)

Figure 3-1. Refraction of light at the interface between two materials. (a) Case 1, light bending away from the

normal. (b) Case 2, light bending towards the normal. (c) Case 3, light not being bent at all.

PROCEDURE

Open the link below to the simulated refraction experiment:

https://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html

(1) Under “Bending Light” in the PhET simulation, select “More Tools.”

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(2) You will see a laser pointer which is aimed at an interface between two different materials (defaults to air and glass). Turn the laser on, and try rotating it to change the angle of incidence. Make sure you can

identify the incident, reflected, and refracted rays.

(3) On the lower left corner of the screen, check the “Angles” box to show the angles of the incident and refracted rays with respect to the surface normal (the dashed line).

⮚ Q1: What is the index of refraction of the upper material and the lower material (ni and nr)? What is the angle of incidence and the angle of refraction (θi and θr)?

⮚ Q2: Verify that the values you measured obey Snell’s law (show how you did this, should be accurate to 2 decimal places).

(4) For the upper material, make sure “Mystery A” is selected from the “Materials” drop-down menu.

(5) For the lower material, select “Air” from the “Materials” drop-down menu.

(6) In the upper left-hand corner, ensure that the wavelength of your light source is set at 650 nm.

(7) Adjust the position of the light source so that the refracted ray is visible.

(8) Measure the angle of incidence and the angle of refraction.

⮚ Q3: Use your measurements and Snell’s law to determine the index of refraction of the “Mystery A” material.

You should have noticed that with this configuration, there is a range of angles where the incident light is simply

reflected from the surface, and is not refracted at all. This phenomenon is called “total internal reflection,” which

can occur when light moves from a material with a higher index of refraction to a material with a lower index of

refraction (Case 1 shown in Figure 3-1).

The critical angle (θC) is the incident angle at which total internal reflection starts to occur. To find the critical angle,

set the refracted angle to 90° (this is the angle at which the ray is no longer refracted) and apply Snell’s law:

𝑛𝑖 sin(𝜃𝐶 ) = 𝑛𝑟 sin(90

𝑜 ) (3-2)

⮚ Q4: Use Eq. (3-2) and your answer to the previous question to predict the critical angle for interface between the material “Mystery A” and the air.

(9) Starting at an incident angle of 0°, rotate the light source until the refracted ray just disappears (this is when the angle of refraction is 90°).

(10) When this occurs, the angle of incidence is equal to the critical angle.

⮚ Q5: What is the critical angle you found from the simulation for this interface? How does this result compare to your answer for the previous question?

The index of refraction is not the same for all wavelengths (colors) of light. This is why white light, which is a

combination of colors, will separate into a range of colored bands after passing through a prism. This effect is called

dispersion.

(11) From the bottom of the “Bending Light” simulation, select “Prisms.”

(12) Drag the triangular prism into your work area, turn on the light source, and aim the beam at the prism.

(13) You can use the color slider to change the wavelength of the light source. Is the beam refracted more or less with shorter wavelengths?

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(14) On the right side of the screen, switch to the white light source (see the figure to the right).

⮚ Q6: Which colors of the white light beam are bent the most by the prism, and which are bent the least?

⮚ Q7: Is the index of refraction greater for longer or shorter wavelengths?

PART 2: REFRACTION IN CONVEX AND CONCAVE LENSES

PREPARATION

Some other lens-related terminology:

• Principle axis: A line that passes through the center of a lens, and is perpendicular to it.

• Real image: An image formed by a lens is said to be real when light rays actually pass through the image.

• Virtual image: An image formed by a lens is said to be virtual when light rays do not pass through the image.

Two essential characteristics of lenses are focal point and focal length. The focal point is the point where light rays

parallel to the principal axis of the lens cross (or point away from in the case of a diverging or negative lens) after

passing through the lens. The focal length is the distance between the focal point and the center of the lens. For a

lens that has a thickness much less than the radii of curvature, we can use the thin lens equation which relates the

focal length f, to the distance of the object do, and the distance of the image di

1

𝑓 =

1

𝑑𝑖 +

1

𝑑𝑜 (3-3)

Another important quantity of this system is magnification. This is simply the ratio of the height of a resulting image

hi, and the height of the original object ho. This is geometrically the same as the ratio between the distances di, and

do.

𝑀 = ℎ𝑖 ℎ𝑜

= − 𝑑𝑖 𝑑𝑜

(3-4)

PROCEDURE

Open the ‘Lenses’ simulation found at the following link here (For iPad, you can use the link here). You should see

the simulation shown in Figure 3-2. The simulation allows users to modify the focal length of a lens, and the

placement of an object relative to the lens.

Figure 3-2. Geogebra simulation for concave and convex lenses. Note: red numbers do not appear in the simulation.

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There are three rays of light showing how light is refracted by the lens and focuses on the image. These lines are

drawn as follows:

1. Starts parallel to the optical axis and is refracted so that it passes through the point labeled Focus. 2. This ray always runs through the center of the lens and is not refracted by the lens. 3. Moves towards Focus’ and is refracted so that the ray then runs parallel to the optical axis.

Depending on the configuration, you may form a virtual image. When this happens, you will see dashed lines that

trace back from the refracted rays to where the virtual image is formed.

(1) Create a data table similar to Table 3-1 for collecting data.

(2) Place the object on the left side of the lens, and keep the focal length selection dot (Focus’) to the left side of the lens (creating a positive lens). Make sure the focal distance is less than the object distance.

⮚ Q8: Observe the position of the image relative to the object and lens. Does this indicate if the image formed is real or virtual?

(3) With the object still on the left side of the lens, move the focal length selection dot to the right side of the lens to create a negative lens.

⮚ Q9: How is the image formed by the negative lens different from the one formed by the positive lens?

(4) Move the focal length back to the left side of the lens, and place it on the 3rd tick mark.

(5) Click and drag the object so that it is to the left of focus’. Make sure the image is visible.

(6) Use the tick marks to measure the object distance (do), the image distance (di), the object height (ho), the image height (hi), and the focal length (f).

Note that units are not given, so you can treat them as arbitrary units for distance.

(7) Calculate the inverse of the object distance and the image distance.

(8) Use Eq. (3-3) to calculate the focal length of the system.

(9) Use Eq. (3-4) to calculate the magnification of the system.

(10) Move the object back about a tick mark and repeat the measurements and calculations again.

⮚ Q10: How does the difference between where the focal length was placed, and what you measured using Eq. (3-3) compare?

⮚ Q11: Was there more or less magnification as the object was moved farther away, and why?

Table 3-1. Lenses data collection table.

Measured Values Calculated Values

Data Point di do f hi ho 1/di 1/do f M

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2

3