**Audry Alburquerque**

**Abstract:**

The goal of this experiment was to determine how does light react when it travels through different mediums. The student had to answer one question: “How does light react as it goes through lenses and as it traverses liquids?” And her possible hypotheses were: “If I use the Geometric Optics program to see how light reacts when passing through different lenses, then I will see that light either converges, concave lenses, or diverges, concave lenses, because light either reflects or refracts” and “If I use Bending Light software to see how light reacts when passing through a fluid, then I will be able to see that it bends depending on the angle because of the law of refraction and the index of refraction.” In an experiment in which the student used the Geometric Optics program and the Bending Light program, she concluded that her hypothesis was right, because as she changed the mediums in the virtual lab, light’s direction changed.

**Lab 12.8 – Light:**

During this experiment, the student had to find out how does light react as it goes through lenses and as it traverses liquids. In order to answer this question, she created two hypotheses: If I use the Geometric Optics program to see how light reacts when passing through different lenses, then I will see that light either converges, concave lenses, or diverges, concave lenses, because light either reflects or refracts” and “If I use Bending Light software to see how light reacts when passing through a fluid, then I will be able to see that it bends depending on the angle because of the law of refraction and the index of refraction.”

The relationship between the focal length f, image distance di, and object distance do is a formula: 1/ do + 1/di = 1/f. In a spherical mirror, an object or image behind the mirror has negative distance and is virtual.The focal length of a convex mirror is negative and the image distance is always negative. An object placedfarther or closer than the focal point in front of a convex mirror produces a reduced, upright, virtual image. An object that is closer to the concave mirror than the focal point always produces an enlarged and virtual image. An object that is beyond the focal point always produces an inverted, real image. Rays of light that pass through the convex lens move closer together or converge. Rays of light that pass through the concave lens spread out or diverge. (Nirenberg, Kim, & Kim, Sect. 20.2) The Lensmaker’s equation is: P = 1/f = (n-1) (1/R1 – 1/R2 + (n-1) d/nR1R1). The spherometer consists of a base circle of three outer legs, a ring, or the equivalent, having a known radius of the base circle, a central leg, and a reading device for measuring the distance the central leg is moved.(Wikipedia, 2014) Three principal rays form part in the construction of ray diagrams for convex mirrors: a ray that would pass through the focal point is reflected parallel to the principal axis; a ray that is parallel to the principal axis reflects as if in line with the focal point; a ray that would pass through the center of curvature is reflected back upon itself. (Nirenberg, Kim, & Kim, Sect. 20.2) The minimum value that the index of refraction can have is 1. The index of refraction of air is: 1.000293, water: 1.3330, ordinary glass: 1.50, and polycarbonate plastic: 1.5849. (Wikipedia, 2014) The speed of light in a vacuum is 3.00 x 10^{8} m/s. (Nirenberg, Kim, & Kim, Sect. 19.4) The relationship between the speed of light and the index of refraction is the formula: n = c/v. (HyperPhysics, 2012)

**Methods:**

The student used a computer, Geometric Optics simulation program, and Bending light simulation program. She ran both programs: http://phet.colorado.edu/en/simulation/geometric-optics and http://phet.colorado.edu/en/simulation/bending-light and tried to learn how to use them. The student analyzed the differences that exist between a real image and a virtual image. Later, using the ruler, she gathered data to solve for focal distance and magnification of the lens using the mirror formula. Later she opened http://phet.colorado.edu/en/simulation/bending-light and familiarized with the program. She recorded what happened when she changed the index of refraction of one or two materials. The student also analyzed which tool was better for measuring angles, and what beam was better also for the angles. After following each possible step properly, the class ended, so the student had to continue her methods at her house on the following days.

**Results/Data Collection/Calculations:**

Lens’s refractive index (n): 1.8 and the radius of curvature (R): 0.7m.

**Focal distance (f)**

**Distance object (d****o****)**

**Distance image (d****i****)**

**Magnification (m)**

43.5cm

120.0 cm

66.0cm

-0.550

43.5cm

90.0 cm

81.0cm

-0.900

43.5cm

60.0 cm

148.9cm

-2.48

45.5cm

30.0 cm

-88.0cm

2.93

-58.8cm

15.0 cm

-11.9cm

0.793

1/ do + 1/di = 1/f = 1/120.0cm +1/66.0cm = 0.023cm^{-1} = 43.5cm

M = -di/do = -66.0cm/120.0cm = -0.550

1/ do + 1/di = 1/f = 1/90.0cm + 1/81.0cm = 0.023cm^{-1} = 43.5cm

M = -di/do = -81.0cm/90.0cm = -0.900

1/ do + 1/di = 1/f = 1/60.0cm + 1/148.9cm = 0.023cm^{-1} = 43.5cm

M = -di/do = -148.9cm/60.0cm = -2.48

1/ do + 1/di = 1/f = 1/30.0cm + 1/-88.0cm = 0.022cm^{-1} = 45.5cm

M = -di/do = 88.0cm/30.0cm = 2.93

1/ do + 1/di = 1/f = 1/15.0cm + 1/-11.9cm = -0.017cm^{-1} = -58.8cm

M = -di/do = 11.9cm/15.0cm = 0.793

Lens’s refractive index (n): 1.25 and the radius of curvature (R): 0.80m

**Focal distance (f)**

**Distance object (d****o****)**

**Distance image (d****i****)**

**Magnification (m)**

62.5cm

120.0 cm

130.0cm

-1.083

50cm

90.0 cm

110.cm

-1.22

34.5cm

60.0 cm

80.0cm

-1.33

17.9cm

30.0 cm

45.0cm

-1.50

10cm

15.0 cm

30.0cm

-2.00

1/ do + 1/di = 1/f = 1/120.0 + 1/130.0cm = 0.016cm^{-1} = 62.5cm

M = -di/do = -130.0cm/120.0cm = -1.083

1/ do + 1/di = 1/f = 1/90.0cm + 1/110cm = 0.020cm^{-1} = 50cm

M = -di/do = -110cm/90.0cm = -1.22

1/ do + 1/di = 1/f = 1/60.0cm + 1/80.0cm = 0.029cm^{-1} = 34.5cm

M = -di/do = -80.0cm/60.0cm = -1.33

1/ do + 1/di = 1/f = 1/30.0cm + 1/45.0cm = 0.056cm^{-1} = 17.9cm

M = -di/do = -45.0cm/30.0cm = -1.50

1/ do + 1/di = 1/f = 1/15.0cm + 1/30.0cm = 0.100cm^{-1} = 10cm

M = -di/do = -30.0cm/15.0cm = -2.00

**Part 2- Air to Water**

**Angle of Refraction**

**Angle of Incidence**

15Es

20Es

30Es

42**Es**

45Es

60**Es**

60Es

78**Es**

75Es

92Es

90Es

110**Es**

**Analysis/Discussion/Conclusion:**

The main goal of this experiment was to determine how does light react when it travels through different mediums. After she finished the experiment, she learned how light reacts as it goes through lenses and liquids. The student realized that both of her hypothesis were right: “”If I use the Geometric Optics program to see how light reacts when passing through different lenses, then I will see that light either converges, concave lenses, or diverges, concave lenses, because light either reflects or refracts” and “If I use Bending Light software to see how light reacts when passing through a fluid, then I will be able to see that it bends depending on the angle because of the law of refraction and the index of refraction.” Her conclusion was that these hypotheses were right because light does not behave the same through different materials, and the bending of the light that she predicted in her hypotheses matched with the virtual lab. The student learned that with the increasing of the index of refraction of a material, the focal distance decreased. In the Bending Light part when she had to measure angles, the protractor was the best tool. Geometric Optics and Bending Light programs are a little complex, but they are helpful when it comes to understanding how does light act depending on the circumstances.

**References:**

Boundless. (2014). *The Lensmaker’s Equation*. Boundless. Retrieved from https://www.boundless.com/physics/geometric-optics/lenses/the-lensmaker-s-equation/

HyperPhysics. (2012). *Refraction of Light*. C.R. Nave. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/refr.html

Nirenberg, I., Kim, J., & Kim, J. (2013). *CK-12 physics – intermediate*. CK-12 Foundation. Retrieved from http://www.ck12.org/book/CK-12-Physics—Intermediate/r12/section/20.0/

Oocities.org. (2014). *Ray Diagrams Pics*. Oocities.org. Retrieved from http://www.oocities.org/rjwarren_stm/2P4/RayDiagramsPics.gif

Phet. (2013). *Geometric optics*. University of Colorado. Retrieved from http://phet.colorado.edu/en/simulation/geometric-optics

Phet. (2013). *Bending light*. University of Colorado. Retrieved from http://phet.colorado.edu/en/simulation/bending-light

Wikipedia. (January 28, 2014). *List of refractive indices*. Wikimedia Foundation, Inc. Retrieved from http://en.wikipedia.org/wiki/List_of_refractive_indices#List

Wikipedia. (November 18, 2013). *Spherometer*. Wikimedia Foundation, Inc. Retrieved from http://en.wikipedia.org/wiki/Spherometer