light: refraction

refraction of light

the bending of light when it goes from one medium to another obliquely is called refraction of light

cause of refraction of light

refraction of light is due to the fact that the speed of light is different in different media

the greater the difference in speed of light in two media, the greater the amount of reflection

why does a change in speed cause refraction of light

this is due to the wave theory of light

the speed of light waves on one side of a beam light changes a little before the change in speed of light waves on its other side, causing a change in direction of light

optically denser and optically rarer media

denser: medium in which the speed of light is less. it has higher refractive index

rarer: medium in which the speed of light is more. it has lower refractive index

emergent ray

the ray of light which comes back to the original medium is called emergent ray

angle of emergence

the angle which the emergent ray makes with the normal is called angle of emergence

the angle of incidence is equal to angle of emergence (i=e)

lateral displacement

the perpendicular distance between original path of incident ray and emergent ray is called lateral displacement of the emergent ray of light

what happens when light falls perpendicularly on a different medium?

if the incident ray falls normally (or perpendicularly) to a different medium, then there is no bending of light and it goes straight

effects of refraction of light

a stick held obliquely and partly immersed in water appears to be bent at the water surface

an object placed underwater appears to be raised

a pool of water appears less deep than it actually is

when a thick glass slab is placed over print, the letters appear to be raised

stars appear to twinkle on a clear night

=> these phenomena occur because we see virtual images of the objects which is formed by refraction of light

laws of refraction of light

the incident ray, refracted ray and the normal at the point of incidence, all lie in the same plane

the ratio of sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media (snell’s law)

=> sin i/ sin r = constant

refractive index

the value of constant sin i/sin r for a ray of light passing from one medium to another medium is called the refractive index

it can also be called the ratio of speed of light in one medium to the speed in another

it is denoted by ‘n’

absolute refractive index

the refractive index of a medium with respect to vacuum/ air is called absolute refractive index

the absolute refractive index is good for comparison and can thus tell us the light-bending ability of a medium

formula: c/v [c = speed of light in air]

relative refractive index

when light is going from one medium (other than vacuum/air) to another, then the value of refractive index is called relative refractive index

what does refractive index depend on?

nature of the material of the medium

wavelength/ color of the light

what happens when two media are optically the same

there is no bending of light

lenses and their types

it is a piece of transparent glass bound by two spherical surfaces

convex lens: it is thick at the center but thinner at the edges. it is also called a converging lens

concave lens: it is thin at the center but thicker at the edges. it is also called a diverging lens

optical center

it is the center point of a lens

it is denoted by ‘C’

principal axis

it is a line passing through the optical center of a lens and perpendicular to both faces of the lens

principal focus (convex lens)

the point on the principal axis on which light rays parallel to the principal axis converge after passing through the lens is called the principal focus

a lens has two foci, who are at equal distances from the optical center

a convex lens has a real focus

principal focus (concave lens)

the point on the principal axis on which light rays parallel to the principal axis converge (appear to diverge) after passing through the lens is called the principal focus

a lens has two foci, who are at equal distances from the optical center

a concave lens has a virtual focus

focal length

it is the distance between optical center and principal focus of the lens

higher the refractive index, shorter the focal length

rules for obtaining images formed by convex lenses

RULE 1: a ray of light which is parallel to the principal axis, passes through its focus after refraction

RULE 2: a ray of light passing through the optical center retraces its path

RULE 3: a ray of light passing through the focus becomes parallel to the principal axis after reflection

image formation by a convex lens when the object is placed between F and lens

nature of image: virtual and erect

position of image: behind the object

size of image: magnified

image formation by a convex lens when the object is at F

nature of image: real and inverted

position of image: at infinity

size of image: highly magnified

image formation by a convex lens when the object is between F and 2F

nature of image: real and inverted

position of image: beyond 2F (the other 2F)

size of image: magnified

image formation by a convex lens when the object is at 2F

nature of image: real and inverted

position of image: at 2F (the other 2F)

size of image: same size as object

image formation by a convex lens when the object is beyond 2F

nature of image: real and inverted

position of image: between F and 2F

size of image: diminished

image formation by a convex lens when the object is at infinity

nature of image: real and inverted

position of image: at F

size of image: highly diminished

uses of convex lens

used in spectacles to correct vision defects

used in making simple cameras

used as magnifying glass

used in making microscopes, telescopes etc.

new cartesian sign convention

all distances are measured from the optical center of the lens

the distances measured in the same direction as incident light is +

the distances measured against the direction of incident light is -

the distances measured above the principal axis are +

the distances measured below the principal axis are -

sign convention for convex lenses

f: +

u: -

v: - if virtual; + if real

h: +

h’: + if virtual; - if real

rules for obtaining images formed by concave lenses

RULE 1: a ray of light which is parallel to the principal axis appears to be coming from its focus after refraction

RULE 2: a ray of light passing through the optical center retraces its path

RULE 3: a ray of light passing through the focus becomes parallel to the principal axis after refraction

image formation by concave lens when the object is anywhere between O and infinity

nature of image: virtual and erect

position of image: between O and F

size of image: diminished

NOTE: further the object, smaller the image

image formation by concave lens when the object is at infinity

nature of image: virtual and erect

position of image: at F

size of image: highly diminished

how to distinguish between convex and concave lenses

if the image of a close of object is enlarged, it is a convex lens and if it is diminished, it is a concave lens

uses of concave lens

used in spectacles

used as eye-lens in galilean telescope

used in wide-angle spyhole in doors

sign convention in concave lens

f: -

u: -

v: -

h: +

h’: +

power of a lens

it is a measure of the degree of convergence or divergence of light rays in lenses. OR it is defined as the reciprocal of its focal length in metres

its SI unit is diaptre (D)

a lens of short focal length has more power whereas a lens of long focal length has less power

convex lenses have positive power while concave lenses have negative power