Lecture 22: Mirrors and Snell's Law

23.1-23.5 Giancoli

ray model of light

light travels in straight lines, we represent light using rays which are straight lines emanating from each single point on an object, these rays entering the eye makes the image

Law of Reflection

angle of reflection is equal to the angle of incidence

when an object is placed in front of a plane mirror, its image appears to be…

behind the mirror

plane mirror image

Types of images

real image

virtual image

real image

when light rays actually pass through the image location

virtual image

when the light rays do not pass through the image location

Types of spherical mirrors

• convex

• concave

concave mirrors: parallel rays after reflection from a mirror converge at a point called…

the focal point

mirror equation

• relates the object distance, image distance, and focal length of the mirror

1/d0 + 1/di = 1/f

• 1/distance of object + 1/distance of reflected image = 1/distance to focal point

magnification equation

m = hi/ho = -di/do

• hi = height of image

• ho = height of the object

• di = image distance

• do = object distance

NOTE: negative sign indicates that the image is inverted

Convex mirrors

convex and concave mirrors table relating to mirror equation and magnification

If you look at yourself in a Christmas three ball with a diameter of 9cm when your face is 30 cm away from it, where is your image, is it real of virtual, is it upright or inverted?

real or virtual

to get radius, 9/2 = 4.5 cm

since mirror is convex, focal length will be neg and given by

• f = r/2 = 4.5/2 = -2.25

object distance = distance from face to mirror

• do = +30 cm

1/do + 1/di = 1/f

1/30 + 1/di = 1/-2.25 —> di = -2.1 cm

since distance is negative, the image is virtual (appears behind the mirror)

magnification

m= ho​/hi​​= −do​/di​​

m = -(2.1/30) = 0.07

therefore image is upright (positive magnification)

image is smaller by 7%

a concave mirror has a radius of 42 cm. an object is laced 84 cm in front of the mirror’s principal axis. Where is the image located?

f = r/2 = 42/2 - 21 cm

1/do + 1/di = 1/f

1/84 + 1/di = 1/21

di = 28

m = hi/ho = -di/do

m = -28/84 = -0.333

a dentist holds a concave mirror of r = 50 mm at a distance of 20 mm from a cavity in a tooth, what is the image of the cavity, what is the size of the image

1/do + 1/di = 1/f

• f = d/2 = 50/2 = 25

• 1/20 + 1/di = 1/25

• di = -100 mm

m= -di/do = -(-100/20) = 5

image is virtual

index of refraction

• light slows down when traveling through any medium

• ratio of the speed of light in vacuum to the speed of light n the medium is called the index of refraction of he medium

• n = c/v

  • c = speed of light in vacuum

  • v = speed of light in medium

The higher the index of refraction the…

slower light will travel through that material

what is refraction

• light changes direction when crossing a boundary from one medium to another

refraction formula and theory

the angle of refraction depends on the speed of light in the two mediums (media) and the incident angle

• sin theta1/sin theta2 = v1/v2

snells law

v = c/n

• c = speed of light in vacuum

• v = speed of light in medium

• n = index of refraction

THEREFORE:

n1 sin(theta1) = n2 sin(theta2) [snell’s law]

• n2 > n1 → towards the normal line

• n2 < n1 → away from the normal line

a flashlight beam strikes a surface of a pane of glass (n =1.52) at 63 degrees to the normal, what is the angle of refraction

total internal reflection - fiber optics

• when light passes into a medium whose n2 < n1, then theta-r > theta-i

• there is an angle theta-i for which theta-r = 90 degrees

• this is called the critical angle theta-c

• if theta-i is larger than theta-c, no transmission occurs

• this is called total internal reflection

n1 sin theta(1) = n2 sin theta(2)

• as theta(1) increases so does theta(2)

• at critical angle → theta(2) = 90 degrees

• n1sin theta-c = n2 sin90

• theta-c = inverse sine(n2/n1)

  • when theta 1 > theta-c LIGHT IS TOTALLY REFLECTED BACK INTO THE SAME MEDIUM

total internal reflection is the

principle behind fiber optics

Light will be transmitted along the fiber even if it is not

straight

image can be formed using

multiple small fibres