Unit 3 - Lesson 6: Refractive Index and Snell's Law Flashcards
What must you know to calculate the angle of refraction?
The refractive index
What does the refractive index tell us?
The refractive index tells us how fast light travels through a material. This can tell us how much the material will refract a wave.
What letter do we use to represent refractive index?
(n)
what formulas do we use to calculate refractive index?
refractive index = speed of light in a vacuum/speed of light in that material
n = c/v
AND
n = sin i/sin r
if an exam asks you for the definition of refractive index, what would you write?
n = sin i/sin r
Which formula (rearranged) can we use to calculate the angle of refraction using Snell’s law? What buttons do we need on a calculator?
n = sin i/sin r
Because n is reflective index, i is angle of incidence, and r is angle of refraction.
To calculate r (angle of refraction), you need to be able to use sin() on a calculator. You will also need a button for sin^-1().
How do you calculate the angle of refraction?
- Write out the formula for Snell’s law. n = sin i/sin r
- Multiply both sides by sin r. This removes sin r from the right:
n x sin r = sin i/sin r x sin r. simplified: n x sin r = sin i - Divide both sides by n. This removes n from the left side:
n x sin r/n = sin i/n. simplified: sin r = sin i/n - Remove sin from the left. Multiply the right by sin^-1:
sin r = sin^-1 (sin(i)/n)
What is the triangle for n = sin i/sin r?
Top of the triangle is sin i.
Bottom left of the triangle is n.
Bottom right of the triangle is sin r.
If the angle of incidence is 20 degrees and n is 1.7, what is the angle of refraction?
sin r = sin^-1 (sin(20)/1.7) = 11.6 degrees (3sf)
Rearrange the formula for Snell’s law to find the angle of incidence.
sin (i) / sin (r) = n
sin (r) x n = sin (i)
sin^-1 (sin (r) x n) = sin (i)
If n = 1.1 and r = 4 degrees, what is the angle of incidence? Use Snell’s law to calculate this.
sin (i) / sin (r) = n
sin (i) / sin (4) = 1.1
sin (4) / 1.1 = sin (i)
0.077 = sin (i)
sin^-1 (0.077) = i
i = 4.4 degrees
What equipment do you need for the core practical: investigating the refractive index?
Ruler.
Pencil.
Paper.
Protractor.
Appropriate light source (e.g. ray box, light box or laser). We can’t use a torch in its standard form as the light rays are too dispersed.
What are the instructions for the core practical: investigating the refractive index?
Measure the angle of incidence/angle of refraction.
Use the Snell’s law formula to find n (substitute in the values for i and r). This is the refractive index of the glass.
Draw around a glass or perspex rectangular block on paper.
Remove the block and draw in a normal line.
Place the block back and direct a light ray at the block so it meets the block at the normal.
Use pins or draw on crosses to label where the light enters and leaves the block.
Remove the block and draw in the lines where the ray passes. Measure i and r.
How can we make our results reliable for the core practical: investigating the refractive index?
Repeat for different angles of incidence and calculate a mean.
Alternatively, repeat for different angles of incidence and plot a graph of sin i against sin r (for all your angle of incidence readings). Then calculate n from the gradient of this graph.
(gradient (m) = y2 - y1/x2 - x1)
(explanation: with the co-ordinates 6,5, y2 would be 5 and x2 would be 6.)
How do we calculate refractive index (n) from a graph?
- Choose two points on the plot line. Mark with a cross.
- Draw a triangle using these two points.
- Find the values for x and y (reading off the x and y axis).
- Substitute the values into:
gradient (n) = change in y/change in x
FOR EXAMPLE:
gradient (n) = 0.20/0.13 = 1.54
https://i.pinimg.com/736x/7b/ac/91/7bac912ebc2f35a512d4bd1fe7715708.jpg
Why do we have to switch sin (i) and sin (r) axes?
The independent variable (sin i) should be on the x axis and the dependant variable on the y axis. However, we have had to switch them to find n. Therefore, if asked in the exam to name the dependant or independent variable, we can’t use the graph in the normal way to find this.
How do we find n from a graph with sin (i) on the x axis?
Find the gradient using the method above. Then take the inverse (1 divided by the gradient).
What is the refractive index (n) of glass?
1.5
What is the refractive index (n) of water?
1.33
What is the refractive index (n) of air?
1
What is the refractive index (n) of diamond?
2.4
What is the refractive index (n) of sapphire?
1.8
What is the refractive index (n) of acrylic?
1.5
