Refraction of light

objectives: defining refraction, angle of incidence, angle of refraction / snells law / apparent death / refraction at plane surfaces / refraction at curved surfaces

refraction definition

when a ray of light is incident on a surface some of it will be reflected, and some absorbed

the direction of the ray inside the surface (glass) is different to that of the incident ray#

this change of direction of the ray at the surface is - refraction

using the diagram explain what happens when an incident ray of light is refracted at the plane boundary between air and glass, and identify the angles

the incident ray hits the surface and travels through the surface - refracts

i = angle of incidence

i’ = angle of refraction

why is the refracted ray bent more towards the normal in the above figure

this is what we expect when light travels from a less dense medium (air) to a more dense medium (glass)

using a diagram explain what happens when a ray of light travels from a more dense medium (glass) to a less dense medium (air)

the refracted ray will be bent more AWAY from the normal

what is snells law

the ratio of sine of the angle of incidence to the sine of the angle of refraction is a constant for any pair of media

sin i / sin i’ = constant

what is the constant referred to as

the refractive index (n)

what is refractive index

refractive index, n = velocity of light in vacuum / velocity of light in medium

alternative way of writing Snells law

n sin i = n’ sin i’

n = refractive index of first medium

i = angle of incidence

n’ = refractive index of second medium

i’ = angle of refraction

what is apparent depth

when the depth of water appears to be less deep (more shallow) than it actually is - this is due to the refraction of light rays at the water surface - when light passes from a denser medium (water) to a less dense medium (air), causing objects to appear at a shallower depth than they actually are

this can make objects appear shallower underwater than they actually are as our eyes perceive the bending of light when it moves from water to air

this is also why a straw partly immersed in water appears bent

refraction by parallel sided media: what happens when light travels through a parallel sided medium (glass)

incident ray of light hits the surface (glass) and is refracted and the light ray that emerges is called the emergent ray

the emergent ray is parallel to the incidence ray but it is displaced sideways by a distance (s) due to refraction

overall effect for my own understanding : the light changes direction slightly when it goes in and out, but it exits in the same direction it was originally traveling, just shifted a bit to the side.

what is the lateral displacement of the ray

referred to as (s)

the sideways of displacement of light

the distance that the emergent ray is displaced sideways by

simple terms: "sideways distance" between where the light would have gone straight and where it actually exits.

equation for lateral displacement (s)

[ d sin (i-i’) ] / cos i’

example of 2 surfaces that are not parallel

prism

common example of a curved refracting surface

spherical surfaces

can either be concave or convex

effect of convex and concave surfaces on the light rays

convex - causes light rays to converge

concave - causes light rays to diverge

to recap what is the equation for vergence

L = 1 / l

what is the equation for reduced vergence

L = n / l

because we take refractive index into account we called it REDUCED vergence

what is the paraxial equation for refraction at spherical surfaces

n’ - n / r = n / l - n’ / l’

n = refractive index of first medium

n’ = refractive index of second medium

r = radius of curvature

l = object distance

l’ = image distance

how can we re write the above equation including F

n’ - n / r = L - L’ = F

F - power of surface

L - object vergence

L’ - image vergence

we use the above formula when we want to know the power of a surface

paraxial equation for refraction at spherical surfaces - to calculate the linear magnification

m = h’ / h = L / L’

m = linear magnification

h = height of object

h’ = height of image

sign conventions : angles

angles are measured as acute angles

angles measured clockwise = negative sign -

angles measured anticlockwise = positive sign +