1.15 - Transmission and reflection of waves
● Waves can be transmitted and reflected at an interface between media
Refraction
● Occurs when:
○ Waves pass into different media (of different optical density)
○ Waves change direction/speed/wavelength (frequency unchanged)
○ 0˚ < angle of incidence < 90˚
● When waves enter denser medium, wavefronts get shorter and bound up
● ***Snell’s law (including derivation):
v 1 ( speed ∈medium1)
n (refractive index, from medium 1 to medium 2) =
1 2
v 2 ( speed ∈medium2)
sin θ1 (angle of incidence)
n =
1 2
sin θ2 (angle of refraction)
c(speed of light −absolute ,∈air ) sin i(angle of incidence)
∵ n= = where n> 1
v (speed ∈medium) sin r ( angleof refraction)
c 1
○ ∵ c is constant, ∴ n= can be written as n ∝
v v
c c
n1 (refractive index of medium1)= , n2 (refractive index of medium2)=
v1 v2
n2 v 1 sin θ 1
∴ = =❑1 n 2=
n1 v 2 sin θ 2
n1sinθ1 = n2sinθ2
● How to measure refractive index of a solid material:
1. Place material on sheet of plain paper
2. Draw line of normal perpendicular to edge of material
3. Emit beam of ray through material
4. Trace paths of which the ray travelled
5. Do repeats of different angles in which the beam of ray is emitted, record
angles of incidence + angles of refraction
6. Plot graph of sin i over sin r, gradient is refractive index
Total internal reflection
● Applying Snell’s law (n1sinθ1 = n2sinθ2),
n1 sin θ 2
= where θ 1 is critical angle , θ2 is angleof refraction∧¿ 90 ˚
n2 sin θ 1
∵ sinθ1 = sinC, sinθ2 = sin90˚ = 1
1 1
∴ n1 = , ***sin C=
sin C n1
n1 sin C n1
ALSO = →sin C= where n1 <n2
n2 sin 90˚ n2
● ***Critical angle: smallest angle of incidence for total internal reflection to occur
1
, ● Total internal reflection ONLY happens from denser to rarer medium (incidence angle
< refraction angle)/if incidence angle > critical angle
○ Greater refractive index, optically denser, lower wave speed
● Derivation of critical angle equation:
n1sinθ1 = n2sinθ2
n2
sinθ1 = sinθ2 where θ1 is critical angle
n1
If rarer medium is air, n2 = 1
1
sinθ1 = sinθ2
n1
If θ2 = 90˚, sinθ2 = 1 {sinθ ⊁ 1}
θ1 = C (critical angle)
1
∴ sinC = //
n1
● In fibre optics cables, outer material has low refractive index and inner has high
refractive index (meaning that critical angle is small so light can TIR easily)
○ As light travels, its intensity decreases, ∴ we try to get as little
bouncing as possible (so to reduce energy loss + extend travelling
distance of light)
Lenses
1
● *** P(lens power[dioptres , D])=
f (focal length[m])
● *** Σ P=P1 + P2+ P 3 .. .
Ray diagrams
● Convex lens - image forms after lens
Concave lens - image forms before lens
● Real image - formed by actual intersection of parallel & centre rays, can be formed
on a screen; light rays converge and meet at a point (where the image is formed)
Virtual image - formed when parallel & centre rays “appear to be” originating from a
point but does not actually meet, can still be detected by human eyes BUT cannot
form on a screen (can ONLY be seen by looking directly through lens)
● Images can be:
○ Real/virtual
○ Upright/inverted
○ Magnified/diminished/life-size
● ***Principal focal point: point when incoming parallel rays meet after refraction
through a convex lens/point from which incoming parallel rays appear to diverge from
after refraction through a concave lens
● ***Focal length: distance from centre of lens to focal points (principal foci) of lens
1 1 1
(SBA) image distance when object is at infinity, ie + = , when u = ∞, v = f
u v f
2
● Waves can be transmitted and reflected at an interface between media
Refraction
● Occurs when:
○ Waves pass into different media (of different optical density)
○ Waves change direction/speed/wavelength (frequency unchanged)
○ 0˚ < angle of incidence < 90˚
● When waves enter denser medium, wavefronts get shorter and bound up
● ***Snell’s law (including derivation):
v 1 ( speed ∈medium1)
n (refractive index, from medium 1 to medium 2) =
1 2
v 2 ( speed ∈medium2)
sin θ1 (angle of incidence)
n =
1 2
sin θ2 (angle of refraction)
c(speed of light −absolute ,∈air ) sin i(angle of incidence)
∵ n= = where n> 1
v (speed ∈medium) sin r ( angleof refraction)
c 1
○ ∵ c is constant, ∴ n= can be written as n ∝
v v
c c
n1 (refractive index of medium1)= , n2 (refractive index of medium2)=
v1 v2
n2 v 1 sin θ 1
∴ = =❑1 n 2=
n1 v 2 sin θ 2
n1sinθ1 = n2sinθ2
● How to measure refractive index of a solid material:
1. Place material on sheet of plain paper
2. Draw line of normal perpendicular to edge of material
3. Emit beam of ray through material
4. Trace paths of which the ray travelled
5. Do repeats of different angles in which the beam of ray is emitted, record
angles of incidence + angles of refraction
6. Plot graph of sin i over sin r, gradient is refractive index
Total internal reflection
● Applying Snell’s law (n1sinθ1 = n2sinθ2),
n1 sin θ 2
= where θ 1 is critical angle , θ2 is angleof refraction∧¿ 90 ˚
n2 sin θ 1
∵ sinθ1 = sinC, sinθ2 = sin90˚ = 1
1 1
∴ n1 = , ***sin C=
sin C n1
n1 sin C n1
ALSO = →sin C= where n1 <n2
n2 sin 90˚ n2
● ***Critical angle: smallest angle of incidence for total internal reflection to occur
1
, ● Total internal reflection ONLY happens from denser to rarer medium (incidence angle
< refraction angle)/if incidence angle > critical angle
○ Greater refractive index, optically denser, lower wave speed
● Derivation of critical angle equation:
n1sinθ1 = n2sinθ2
n2
sinθ1 = sinθ2 where θ1 is critical angle
n1
If rarer medium is air, n2 = 1
1
sinθ1 = sinθ2
n1
If θ2 = 90˚, sinθ2 = 1 {sinθ ⊁ 1}
θ1 = C (critical angle)
1
∴ sinC = //
n1
● In fibre optics cables, outer material has low refractive index and inner has high
refractive index (meaning that critical angle is small so light can TIR easily)
○ As light travels, its intensity decreases, ∴ we try to get as little
bouncing as possible (so to reduce energy loss + extend travelling
distance of light)
Lenses
1
● *** P(lens power[dioptres , D])=
f (focal length[m])
● *** Σ P=P1 + P2+ P 3 .. .
Ray diagrams
● Convex lens - image forms after lens
Concave lens - image forms before lens
● Real image - formed by actual intersection of parallel & centre rays, can be formed
on a screen; light rays converge and meet at a point (where the image is formed)
Virtual image - formed when parallel & centre rays “appear to be” originating from a
point but does not actually meet, can still be detected by human eyes BUT cannot
form on a screen (can ONLY be seen by looking directly through lens)
● Images can be:
○ Real/virtual
○ Upright/inverted
○ Magnified/diminished/life-size
● ***Principal focal point: point when incoming parallel rays meet after refraction
through a convex lens/point from which incoming parallel rays appear to diverge from
after refraction through a concave lens
● ***Focal length: distance from centre of lens to focal points (principal foci) of lens
1 1 1
(SBA) image distance when object is at infinity, ie + = , when u = ∞, v = f
u v f
2
