Physics 1 – Plane Refraction
Plane Refraction
Aims
 To investigate refraction at a plane surface.
 To understand Snell’s law and refractive index.
Part 1: Tutorial Question (20 mins)
A parallel sided block of thickness t is made of material of refractive index n and a ray
normal to the surface emerges at a point P as shown below in figure 1.1.
A
t
B
t
normal
θ1
P

y
nB
nA
nB
nA
Figure 1.1
1.1
1.2
1.3
As the block is tilted explain why the displaced beam is always parallel to the
incident one.
Draw figure 1.1B and mark on it the angle , the angle to the normal inside
the block. Hence, show by geometry the angle 
Using the information obtained from question 1.2 and by considering the
angles and sides of the two triangles depicted within the block below


t

y

nB
nA
Figure 1.2
show that if the angle of incidence is  the point of emergence P will move a
distance:


cos 1

y  t sin 1 1 
2
2

n B  sin 1 

Hints:
1
Physics 1 – Plane Refraction
Remember the relationship; sin( A  B)  sin A cos B  cos A sin B .
And, n A sin  A  nB sin  B
Also, n A = nAir =1.
Part 2: Taking Measurements (20 mins)
 Setup the apparatus as in Figure 1.1B and use graph paper to draw the point of
incidence and departure.
 Next, remove the plastic block and join up the lines to produce a schematic similar
to 1.1B above.
 Using a protractor, or by trigonometry, determine all the relevant angles.
2.1
From your measured data calculate an estimate for the refractive index of the
plastic.
2.2
With the angle(s) and length(s) you have just measured, use the equation
above to determine a value for the lateral displacement y and compare it with
your measurement.
2.3
Using the formula for the lateral displacement, y, show by algebraic
manipulation that y will tend to zero as θ1 approaches zero or as nB tends to 1.
Part 3: The Prism (10 mins)
 This time place a new sheet of graph paper on the laser baseboard and place on the
equilateral prism so that one of the sides is parallel to the path of the beam inside
the prism, as in Figure 1.2.


A/2
nB
nA
Figure 1.2
 By making small rotations of the prism, observe that in this symmetrical situation
the angle of deviation,  , is a minimum. Leave the prism set at the minimum
deviation setting and measure .
A 
 A
  n sin   .
 2 
2
3.1

Show that 2 1  A   , and hence that sin 
3.2
Given that the prism is a 60º equilateral triangle, use your measurement of  to
calculate the refractive index of the block.
2
Physics 1 – Plane Refraction
Further Work
The following questions are related to the topic covered by this experimental tutorial.
 Exercise book questions L20 – L23.
 Mastering Physics: Optics 1 (first three parts)
3
Physics 1 – Plane Refraction
Demonstrators' Answers, Hints, Marking Scheme and Equipment List
Marking Scheme
Section
1.1
1.2
1.3
2.1
2.2
2.3
3.1
3.2
Discretionary mark
TOTAL
Mark
1
1
2
1
1
1
1
1
1
10
Answers
1.1
The angle the light is refracted in the block will be the same at the opposite
side, therefore emitting the ray parallel to the incoming ray.









refer to figure 1.2:
we know
y
Hyp

 y  Hyp  sin( 1   2 )
sin( 1   2 ) 

t
Hyp

t
 Hyp 
cos  2
cos  2 
also


4
Physics 1 – Plane Refraction
so
y
t sin( 1   2 )
cos  2

t (sin 1 cos  2  cos 1 sin  2 )
cos  2
 cos 1 sin  2 ) 
 t sin 1 1 

 sin 1 cos  2 
n1 sin 1  n2 sin  2
but
so
knowing


cos 1 sin  2 ) 
y  t sin 1 1 

 n2 sin  2 cos  2 

cos 1 
 t sin 1 1 

 n2 cos  2 
sin2cos2
finally using snell’s law
2.1
See graph paper – first page
2.2
See graph paper – first page
2.3
y tends to zero.
3.1
See graph paper – second page
3.2
See graph paper – second page
i.e.
cos  1 - sin 2 


cos 1
y  t sin 1 1 

 n2 1 - sin 2 2 


cos 1


 t sin 1 1 
2
2

n2 - sin  1 

  0 0 , sin 1  0 ,  y  0
nB  1 n 2  sin 2   1  sin 2   cos 2 
 cos  
 y  t sin 1 1 
 cos  
 t sin 1 1  1
0
5
Physics 1 – Plane Refraction
6
Physics 1 – Plane Refraction
7
Physics 1 – Plane Refraction
Equipment list:
Laser-board with fitted laser and power supply
Box of Perspex blocks
Graph paper
Protractor
Ruler
8