lab report

Lab Report: reflection and Refraction
Name
Institution Affiliation

Introduction
Goals
The goals of experiments were
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.
Introduction
The propagation and behavior of light rays and wavefronts through space can be demonstrated through reflection and refraction. Reflection describes the bouncing back of light at an interface between two such that the wavefront returns to the medium of origin. The phenomena are described using the laws of reflection which states that the angle at which a ray is incident on a plain surface is equivalent to the angle at which the same ray is reflected. Also, the incident ray and the reflected ray as well as the normal, all lie on the same surface.
On the other hand, when light waves pass through transparent media of different densities, the direction of the wave is changed as a result of a change in speed. The aspect of refraction can be described using the law of refraction (Snell’s law) which is illustrated by the equation
n1sin θ1=n1sin θ2 Whereby n is the refractive index of the medium and θ is the corresponding angle.

Hypothesis
The incidence and reflected rays on a plane surface are equal
The radius of curvature is twice the focal length
The incident ray, the normal, and the refracted ray lie in the same plane
Materials
One ray box, two multi-mirrors, 1 Lucite semi-circular lens, one rotating ray table, one metric ruler, and a Graph paper
Procedure
Exercise 1: Reflection from a plane surface
The plastic mask on the front of the ray box was rotated and adjusted to give a single ray. The ray box was raised to the level of the rotating ray table and the rolled–up piece of paper tape was used in joining the rotating ray table. After aligning the plane mirror at an angle of ninety degrees, they are placed at the center of the ray table were set at the center of the ray table aligned perpendicular to the ray light. The incident and reflected angles were measured and the data recorded. The Lucite semicircle is then rotated such that the incoming rays penetrate the Lucite from the curved side and the incident and reflected rays are measured and recorded.
Data
Angle of Incidence (o) Angle of Reflection (o)
10 20
20 40
30 60
40 80
50 100
60 120
70 140
80 160
Exercise 2: Reflection from Two Plane Surfaces at Right Angles
Using the same setup of the ray box as in exercise 1, two plane mirrors were placed at right angles to each in an L-shaped formation on the paper. The ray box was then set up such that the single rays impinged on the front of the mirror at an incident angle of 45 degrees. The incident angles of the incoming rays were then varied and the paths of the incident and reflected marked.
Exercise 3: Focal Length of a Concave Cylindrical Mirror
The radius of curvature of the mirror was first determined by tracing the edge of the mirror on a paper. The radius of the circle was measured using a ruler.
The ray box was then adjusted to give parallel rays. After adjusting the ray box, a graph paper was placed in front of the ray box, and the multi-mirrors concave reflective surface was placed facing the ray box. The position of the mirror was outlined on a paper, and the path of the incident and reflected rays were traced. The focal length of the concave mirror was determined from the ray drawing and compared with the theoretical focal length.
Data
Radius of curvature is 11.3cm
Focal length is 5.6cm
Exercise 5: To calculate the “index of refraction” for Lucite from the data.
A single slit mask was selected on the ray box and the incoming ray aligned along a straight line through the center point of the rotating ray table. The flat face of the Lucite was set at an angle of ninety degrees on the path of the ray, and the path of the incoming and outgoing ray traced visually. The incident angles were then varied from 100 to 800 in increments of 100 by moving the ray table and the data recorded.
Data
Flat to round
Angle of Incidence( o) Angle of Reflection (o)
10 7
20 14
30 21
40 28
50 33
60 37
70 40
80 41

Round to flat
Angle of Incidence( o) Angle of Reflection (o)
10 15
20 30
30 45
40 70
Critical angle is at 45o
50 140
60 130
70 120
80 110
Analysis
Index of refraction of the Lucite
From snells law, n1sin θ1=n1sin θ2For the flat to round, nasinθi=nlsinθrLikewise aηl = 1gηanl=nasinθisinθrnl=nasinθisinθr=1.0029×sin10sin7=1.42For the round to flat nlsin θi=nasin θrnl=1lηa=sinθrnasini=sin151.0029×sin10Flat to round
Angle of Incidence( o) Angle of Reflection (o) Refractive index nasinθisinθr10 7 1.43
20 14 1.42
30 21 1.4
40 28 1.4
50 33 1.4
60 37 1.44
70 40 1.46
80 41 1.50

Round to flat
Angle of Incidence( o) Angle of Reflection (o) Refractive index
nl=1lηa=sinθrnasinθi10 15 1.49
20 30 1.46
30 45 1.41
40 70 1.46
Critical angle is at 45o 50 140 0.83
60 130 0.88
70 120 0.92
80 110 0.95

Discussion
The data recorded in exercise one does not support the law of reflection since the angle of the reflected ray is twice the angle of the incident ray. In exercise two, the incident angle of the inclined plane was 450 while the angle of reflection obtained from the experiment was 44.2 and 44.8. Thus, the results prove that the angle between the incident ray and the normal is equal to the angle between the reflected ray and the normal for plane mirrors inclined perpendicularly. The data in exercise five supports Snell’s law as the value of the refractive index obtained from both flat to round, and round experiment is close to the theoretical value of 1.5 (Elert 2017). The focal length obtained in exercise three was 5.6cm which is half the radius of curvature which was 11.3cm.
Conclusion
The purpose of the experiment was to verify the law of reflection and Snell’s law of refraction. From the experiment we found that the angle of incidence is equal to the angle of reflection, the radius of curvature is twice the focal length, and the incident ray, the normal to the boundary, and the refracted ray lie in the same plane thus verifying our hypothesis.

References
Elert, G. (2017). The physics hypertextbook. Brooklyn, N.Y: Glenn Elert. Retrieved (February 3, 2018) https://hypertextbook.com/facts/2005/EmreErdal.shtml