The light is transmitted back into air at an angle of refraction θ2 -θ1. You can ...
The index of refraction of the prism can be calculated using the Snell's law for the.
Laboratory #9
Phys 2426
Dr. Cristian Bahrim
REFRACTIVE INDEX AND DISPERSION CURVE OF DISPERSION FOR A PRISM
Experiment #1
You will use a setup that includes a triangular glass prism 30-60-90 degree mounted on a rectangular prism. A rectangular block is used for checking the alignment of three lasers: blue, green and red. The laser beams should be perpendicular on the rectangular prism and on the board. Light of wavelength λ is at normal incidence on the bottom face of the triangular prism, and therefore, the transmitted beam is not deviated until it reaches the upper face. On the upper face of the prism the light is incident at 30 degrees (why?).
y
Board
B
A
θ2 − θ1 θ1
L
θ2 C
θ1 LASERS
The light is transmitted back into air at an angle of refraction θ2 -θ1. You can find this angle from the right triangle ABC: tan (θ 2 − θ1 ) =
y , where θ1 = 30 degree. L
(1)
You need to measure the distances y and L, and to calculate the angle θ2 with the formula: y L
θ 2 = θ1 + tan −1
(2)
The index of refraction of the prism can be calculated using the Snell’s law for the upper face of the triangular prism: n prism sin θ 1 = n air sin θ 2
(3)
Fill out the table below and calculate the index of refraction of the prism for each λ. Color
λ [nm]
Blue
475
Green
543
Red
633
L [m]
y [m]
Obs: Take n air = 1 . 1
θ2 [deg.]
nprism
Experiment #2
REFRACTION THROUGH A TRIANGULAR PRISM
In this lab you will measure the index of refraction of a plastic material using a radiation of 633 nm from a HeNe laser#. The material will be in the form of a 30 – 60 – 90 triangular prism. Experimental procedure: Put the triangular prism on a wooden panel with a white paper under the prism. Place the prism in the center of the paper. Orient the triangular prism with the right face toward the laser, so that the laser beam is at normal incidence on the right face of the prism as shown in Fig.1. At normal incidence the reflected laser beam comes back into the laser! Trace the outline of the prism using a sharp pencil. Use the pencil to locate the incident ray (on the front face of the prism) and the two exiting rays (on the opposite face and the bottom face of the prism). Mark enough dots on the paper in order to get an accurate and long enough ray. Remove the block and draw a straight line through the marks you made on either side of the block. Draw the lines for the exiting rays as long as possible. Use the pencil and find the path of the light through the prism from the entering point to the two exit points. This is going to be your ray diagram. Your drawing should be like in Fig. 1.
α
Laser
Laser α
Fig.1
Fig.2 Arrangement 2.
Arrangement 1 - A ray diagram.
Each student should draw a ray diagram for the two orientations of the prism. #
Safety precaution: your eye!
Never look directly into the laser beam or its reflections because it can damage
2
Data acquisition: Measure the angles of refraction on the right face (a) and the bottom face (b) in the Experiment 1 (Fig. 1), and on the bottom face (c) in the Experiment 2 (Fig. 2). The angles should be measured with respect to the normal on each face of the prism. Case
Angle of refraction (degrees)
Index of refraction
(a) (b) (c)
Data analysis: Using Snell’s law, n1 sin θ1 = n2 sin θ 2 , and the law of reflection, θ1 = θ 2 , at each
face of the prism (a, b and c mentioned above), find the formula that allows you to calculate the index of refraction of the plastic prism. Take the index of refraction for air as 1. Fill out the table above.
Using the three trials from above, calculate the average value of the index of
refraction and its standard deviation. Report:
±
n =
.
Search for the total internal reflection: With the arrangement in Fig. 2
rotate your prism until the light through the bottom face of the prism exits along (or parallel with) the surface. In this particular case, the angle of incidence on the bottom face is the critical angle of the plastic-air interface. If the angle of incidence is larger than the critical angle, then the light is totally internal reflected.
3
SOLVE THE FOLLOWING EXERCISE: Consider a 20 – 70 – 90 triangular prism oriented as in the figure 1. Take the value of the index of refraction measured experimentally in the “Experiment 2”. Does a ray emerge through the bottom face of the prism? Why or why not? Your answer should include a ray diagram and convincing calculations.
