Studio Session 8

Refraction and reflection

In this session you will explore the behavior of light at the boundary between two transparent media with different indices of refraction.  A fraction of the incident intensity will be reflected, and the rest of the light will be transmitted.  The direction of propagation of the reflected and transmitted light is given by the laws of reflection and refraction.

imageHow much of the light is reflected and how much is transmitted?

The reflectance R is the ratio of the reflected flux to the incident flux, and the transmittance T is the ratio of the transmitted flux to the incident flux.  Energy conservation requires that R + T = 1 (if there is no absorption).
R and T depend on the indices of refraction of the two media n1 and n2, the angle of incidence θi, and the polarization of the incident light.  We distinguish between p-polarization and s-polarization.

Consider, for example, an air-glass interface as shown.  The plane of incidence contains the normal to the boundary and the incident ray.  The electric field vector E of the incident wave is perpendicular to the direction of propagation and can have a component in the plane of incidence, Ep, and a component perpendicular to the plane of incidence Es.  We have E = Ep+ Es.

imageThe reflectance R depends of the polarization and is given for p-polarization by

Rp = (tan(θi - θt)/tan(θi+ θt))2,

and for s-polarization by

Rs = (sin(θi - θt)/sin(θi+ θt))2.

If θ1 + θ2 = π/2, then tan(θ1 + θ2) = infinite  and Rp = 0.  If light is reflected, it will have s-polarization.  The incident angle at which this happens is called the Brewster angle θB.  We then have

n1sinθB= n2sin((π/2) -θB) = n2cosθB.
tanθB = n2/n1.

Reflection and refraction can result in image formation.  Spherical mirrors form images by reflection.  The mirror equation tells us where the image is formed and if it is real or virtual.

If the magnification is negative, the image is inverted.

Things that always go together for spherical mirrors:

xo and xi are positive for locations in front of the mirror and negative for locations behind the mirror.  R and f are positive for concave and negative for convex mirrors, and f = R/2.

In this session you will explore refraction at a plane interface and image formation by reflection from spherical surfaces.

Equipment needed:

Open a Microsoft Word document to keep a log of your procedures, results and discussions.  This log will become your lab report.  Address the points highlighted in blue.  Answer all questions.


Exploration 1

Use an on-line simulation from the University of Colorado PhET group to explore the bending of light.
Link to the simulation:

Explore the interface!  Click the intro tab. 
(a)  Let red light move from air into water. 
For incident angles θi from to zero 80o in 10 degree steps measure the angle of refraction θt and the reflectance R.
Download this spreadsheet and enter your measured values on sheet 1.

(b)  Design experiments to determine the index of refraction of mystery materials A and B. 

(c)  Design and describe a setup that has the refracted ray bend away from the normal? 

(d)  Click on the prism break tab.  Use red light with a wavelength of 650 nm.  Try to arrange various prisms in such a way, so that the laser beam after total internal reflections moves parallel to the incident beam but in the opposite direction.  Try to use as few pieces as possible.

(e)  Now switch to white light and experiment with various prisms to answer the following questions.

Experiment 1:

In this experiment you will trace the path of a light ray through a block of glass.  You will determine the angle of incidence and the angle of refraction at two air-glass boundaries and use these angles to determine the index of refraction of crown glass.

trial# θair θglass nmeasured w dmeasured dcalc difference (%)

Data Analysis:


Exploration 2:

Explore image formation with spherical mirrors.

Open the simulation at

Investigate 4 different situations and fill out the table on sheet 3 of your spreadsheet.  You choose the radius of curvature R and the object position xo.

case R f xo xi 1/x0 + 1/xi 1/f M image
concave mirror, real image:
|hi| > |ho|
concave mirror, real image:
|hi| < |ho|
concave mirror, virtual image
convex mirror

Convert your log into a session report, certify with you signature that you have actively participated, and hand it to your instructor.