Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: Units Index of refraction of a medium equals the ratio.

Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: Units Index of refraction of a medium equals the ratio of the speed of light in a vacuum and the speed of light in the medium Formula Units

Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: v=f Units m=1 m s s Index of refraction of a medium equals the ratio of the speed of light in a vacuum and the speed of light in the medium Formula Units

Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: v=f Units m=1 m s s Index of refraction of a medium equals the ratio of the speed of light in a vacuum and the speed of light in the medium Formula n = c v Units none=m/s m/s

Waves and optics formula Snell's law: the product of the index of refraction and the sin of the incident angle equals the product of the index of refraction of the second medium and the sin of the refracted angle n 1 sin  1 = n 2 sin  2 The sin of the critical angle ( Above this incident angle, will reflect, but will not refract ) equals the ratio of the index of refraction in the second medium and the index of refraction of the first medium Sin  c = n 2 n 1

Waves and optics formula Formula used for the relationships between image location, object location and the focal length of the lens or mirror 1 + 1 = 1 s i s o f The magnification equals the ration of the image height to the object height or the negative ratio of the image location to the object location M = h i M = - s i h o s o

Waves and Optics Formula The focal length equals the radius of curvature divided by 2 for lens and mirrors f = R 2

Waves and Optics Formula Interference formula single slit equals the d sin  = m  d = single slit width sin f = diffraction angle m = 1,2,.. Minima The position of x m ( 1,2 minima) equals product of the minima, wavelength, distance to screen divided by the slit width x m = m L d

Waves and Optics Formula Interference formula single slit equals the d sin  = m  d = single slit width sin  = diffraction angle m = 1,2,.. Minima The position of x m ( 1,2 minima) equals product of the minima, wavelength, distance to screen divided by the slit width x m = m L d

Waves and Optics Formula Interference formula double or multiple slit equals the d sin  = m  d = distance between slits sin  = diffraction angle m = 1,2,.. Maxima The position of x m ( 1,2 maxima) equals product of the maxima, wavelength, distance to screen divided by the slit width x m = m L d

Plane Mirror

S o equals S i

Plane Mirror S o equals S i Image is upright, virtual, and same size

Plane Mirror So equals Si Image is upright, virtual, and same size

Plane Mirror

Image upright

Plane Mirror Image upright, virtual,

Plane Mirror Image upright, virtual, same size

Plane Mirror Block ½ mirror?

Plane Mirror Block ½ mirror? Image upright, virtual, same size

Plane Mirror Block ½ mirror? Image upright, virtual, same size Dimmer

Shadows

Elicpses – lunar, solar

Convex Mirror S o =10 cm

Convex Mirror S o =10 cm R=6cm f=3cm

Concave Mirror S o =10 cm R=6cm f=+3cm

Concave Mirror

S i = 4.28 cm

Concave Mirror S i = 4.28 cm S o =10 cm R=6cm f=+3cm

Concave Mirror S i = 4.29 cm S o =10 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/10cm = 1/ si S i = 4.29 cm M = - s i / s o = - 4.29 cm 10 cm M = -.429 Inverted Real Smaller

Convex Mirror S i = 4.29 cm S o =10 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/10cm = 1/ si S i = 4.29 cm M = - s i / s o = - 4.29 cm 10 cm M = -.429 Inverted Real Smaller

Concave Mirror S i = 4.29 cm S o =6cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/10cm = 1/ si S i = 4.29 cm M = - s i / s o = - 4.29 cm 10 cm M = -.429 Inverted Real Smaller

Concave Mirror S i = 4.29 cm S o =6 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/6cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = -.429 Inverted Real Smaller

Concave Mirror S i = 4.29 cm S o =6 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/6cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Smaller

Concave Mirror S i = 4.29 cm S o =6 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/6cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Same Size

Concave Mirror S i = 4.29 cm S o =4.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/6cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Same Size

Concave Mirror S i = 4.29 cm S o =4.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/4.5cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Same Size

Concave Mirror S i = 4.29 cm S o =4.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger

Concave Mirror S i = 4.29 cm S o =3.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger Parallel Rays

Concave Mirror S i = 4.29 cm S o =3.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger Parallel Rays - No Image

Concave Mirror S i = 4.29 cm S o =2.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/2.5cm = 1/ si S i = -15.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger

Concave Mirror S i = 4.29 cm S o =2.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/2.5cm = 1/ si S i = -15.0 cm M = - s i / s o = - (-15.0 cm) 2.5 cm M = - 2.0 Inverted Real Larger

Concave Mirror S i = 4.29 cm S o =2.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/2.5cm = 1/ si S i = -15.0 cm M = - s i / s o = - (-15.0 cm) 2.5 cm M =+6.0 Inverted Real Larger

Concave Mirror S i = 4.29 cm S o =2.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/2.5cm = 1/ si S i = -15.0 cm M = - s i / s o = - (-15.0 cm) 2.5 cm M =+6.0 Upright Virtual Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) - 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) - 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) - 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-1.8 cm 4.5 cm M = - 2.0 Inverted Real Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) - 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-1.8 cm 4.5 cm M = +.40 Inverted Real Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) - 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-1.8 cm 4.5 cm M = +.40 Upright Real Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) - 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-1.8 cm 4.5 cm M = +.40 Upright Virtual Larger

Convex Mirror S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) - 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-1.8 cm 4.5 cm M = +.40 Upright Virtual Smaller

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident  refracted

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident  refracted n 1 d incident =n 2 d refracted

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident  refracted n 1 d incident =n 2 d refracted sin  incident =d incident radius sin   efracted = d refracted radius

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident  refracted n 1 d incident =n 2 d refracted sin  incident =d incident radius sin   efracted = d refracted radius Therefore n 1 sin  i ncident =n 2 sin  refracted

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident = 10 0  refracted n 1 d incident =n 2 d refracted sin  incident =d incident radius sin   efracted = d refracted radius Therefore n 1 sin  i ncident =n 2 sin  refracted

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident = 10 0  refracted =7.5 0 n 1 d incident =n 2 d refracted sin  incident =d incident radius sin   efracted = d refracted radius Therefore n 1 sin  i ncident =n 2 sin  refracted

Refraction Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident = 10 0  refracted =7.5 0 n 1 d incident =n 2 d refracted sin  incident =d incident radius sin   efracted = d refracted radius Therefore n 1 sin  i ncident =n 2 sin  refracted n 1 = air = 1.0

Refraction-Snell’s Law Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Index of Refraction (n) n 1 d incident =n 2 d refracted n 1 = air = 1.00 n 1 d incident = n 2 d refracted Therefore d incident / d refracted = n 2 Slope = 1.33=n 2 =n water water air  incident = 10 0  refracted =7.5 0 n 1 d incident =n 2 d refracted sin  incident =d incident radius sin   efracted = d refracted radius Therefore n 1 sin  i ncident =n 2 sin  refracted n 1 = air = 1.0 Sin 10 o = n 2 = n water = 1.33 Sin 7.5 o

Refraction-Snell’s Law Incident Ray Distance to normal 1.33 cm 2.00 cm 2.66 cm 3.33 cm 4.00 cm Refracted Distance to Normal 1.00 cm 1.50 cm 2.00 cm 2.50 cm 3.00 cm Therefore d incident / d refracted = n 2 water air  incident = 10 0  refracted =13.5 0 n 1 sin  i ncident =n 2 sin  refracted n 2 = air = 1.0 n 1 = n water = sin   efracted sin   ncident sin 13.5 o = n 1 = n water = 1.34 sin 10.0 o

Refraction incident   Normal refracted  r incident   refracted  r Towards normal when n i < n r (n=index of refraction or optical density ) Away from normal when n i > n r

Refraction incident   Normal refracted  r incident   refracted  r Towards normal when n i < n r (n=index of refraction or optical density ) Away from normal when n i > n r n air = 1.0

Refraction incident   Normal refracted  r incident   refracted  r Towards normal when n i < n r (n=index of refraction or optical density ) Away from normal when n i > n r n air = 1.0 N glass 1.3

Refraction incident   Normal refracted  r incident   refracted  r Towards normal when n i < n r (n=index of refraction or optical density ) Away from normal when n i > n r velocity of light decreases v = c n Frequency remains the same n = vacuum n n glass = 1.3 n air = 1.0

Refraction incident   Normal refracted  r incident   refracted  r Towards normal when n i < n r (n=index of refraction or optical density ) Away from normal when n i > n r velocity of light decreases v = c n Frequency remains the same n = vacuum n n air = 1.0 n glass = 1.3

Refraction incident   Normal refracted  r incident   refracted  r Towards normal when n i < n r (n=index of refraction or optical density ) Away from normal when n i > n r velocity of light decreases v = c n Frequency remains the same n = vacuum n n air =1.0 n glass = 1.3

Refraction incident   Normal refracted  r incident   refracted  r Away from normal when n i > n r (n=index of refraction or optical density ) Toward normal when n i > n r velocity of light decreases v = c n

Snell’s Law Incident  = 10 o Refracted  = 6.5 o n 1 for air = 1.0 n 2 = ? 10 0 6.5 0 n 1 sin  i = n 2 sin  2 n 1 sin  i = n 2 = 1.0 sin 10 o =1.5 sin  2 sin 6.5 0

Snell’s Law Incident  = 10.0 o Refracted  = 15.4 o n 1 = ? n 2 = 1.0 (air) 10 0 15.4 0 n 1 sin  i = n 2 sin  2 n 1 = n 2 sin  2 = = 1.0 sin 15.4 0 =1.5 sin  1 sin 10.0 0

Snell’s Law Incident  = 15.0 o Refracted  = 23.3 o n 1 = ? n 2 = 1.0 (air) 15 0 23.3 0 n 1 sin  i = n 2 sin  2 n 1 = n 2 sin  2 = = 1.0 sin 23.3 0 =1.5 sin  1 sin 15.0 0

Critical Angle- Total Internal Reflection Incident  = ? If n 1 =1.5 n 2 =n air =1.0 sin  c = n 2 n 1  c = 42 o The larger the difference between n 2 and n 1 the smaller the ratio and the lower the critical angle 30.1 0 n 1 sin  i = n 2 sin  2

Critical Angle- Total Internal Reflection Incident  = ? If n 1 =1.5 n 2 =n air =1.0 sin  c = n 2 =1.0 n 1 1.5  c = 42 o The larger the difference between n 2 and n 1 the smaller the ratio and the lower the critical angle 30.1 0 n 1 sin  i = n 2 sin  2

Snell’s Law Incident  = 20.0 o Refracted  = 31.6 o n 1 = ? n 2 = 1.0 (air) 20.0 0 30.1 0 n 1 sin  i = n 2 sin  2 n 1 = n 2 sin  2 = = 1.0 sin 31.6 0 =1.5 sin  1 sin 20.0 0

Critical Angle- Total Internal Reflection Incident  = ? If n 1 =1.5 n 2 =n air =1.0 sin  c = n 2 n 1  c = 42 o Refracted  = 31.6 o n 1 = ? n 2 = 1.0 (air) 30.1 0 n 1 sin  i = n 2 sin  2

Critical Angle- Total Internal Reflection Incident  = ? If n 1 =1.5 n 2 =n air =1.0 sin  c = n 2 n 1  c = 42 o Any incident angle above that critical angle will only reflect. 30.1 0 n 1 sin  i = n 2 sin  2

Critical Angle- Total Internal Reflection Incident  = ? If n 1 =1.5 n 2 =n air =1.0 sin  c = n 2 n 1  c = 42 o The larger the difference between n 2 and n 1 the smaller the ratio and the lower the critical angle 30.1 0 n 1 sin  i = n 2 sin  2

15 0 Law of Reflection 10.7 o Snell’s law – Refraction n 1 sin  1 = n 2 sin  2 n 1 sin  1 = sin  2 n 2 1.0sin 15 0 = sin  2 1.4 10.7 o =  2 Snell’s law – Refraction n 1 sin f 1 = n 2 sin f 2 n 1 sin f 1 = sin f 2 n 2 1.4sin 36 0 = sin  2 1.0 45.6 o =  2 36 o 45.6 o 1.0 1.4 1.0

15 0 Law of Reflection 10.7 o Snell’s law – Refraction n 1 sin  1 = n 2 sin  2 n 1 sin  1 = sin  2 n 2 1.0sin 15 0 = sin  2 1.4 10.7 o =  2 Snell’s law – Refraction n 1 sin f 1 = n 2 sin f 2 n 1 sin f 1 = sin f 2 n 2 1.4sin 36 0 = sin  2 1.0 45.6 o =  2 36 o 45.6 o 1.0 1.4 1.0 36 o

15 0 Law of Reflection 10.7 o Snell’s law – Refraction n 1 sin  1 = n 2 sin  2 n 1 sin  1 = sin  2 n 2 1.0sin 15 0 = sin  2 1.4 10.7 o =  2 Snell’s law – Refraction n 1 sin f 1 = n 2 sin f 2 n 1 sin f 1 = sin f 2 n 2 1.4sin 36 0 = sin  2 1.0 45.6 o =  2 36 o 45.6 o 1.0 1.4 1.0 36 o Law of Reflection

15 0 Law of Reflection 10.7 o Snell’s law – Refraction n 1 sin  1 = n 2 sin  2 n 1 sin  1 = sin  2 n 2 1.0sin 15 0 = sin  2 1.4 10.7 o =  2 Snell’s law – Refraction n 1 sin f 1 = n 2 sin f 2 n 1 sin f 1 = sin f 2 n 2 1.4sin 36 0 = sin  2 1.0 45.6 o =  2 36 o 45.6 o 1.4 1.0 1.4 1.0 How would the reflection and refraction be different ?

S o =9.0 cm R=6cm f=+3cm Converging Lens S i = 4.29 cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/10cm = 1/ si S i = 4.29 cm M = - s i / s o = - 4.29 cm 10 cm M = -.429 Inverted Real Smaller

Converging Lens S i = 4.29 cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/10cm = 1/ si S i = 4.29 cm M = - s i / s o = - 4.29 cm 10 cm M = -.429 Inverted Real Smaller S o =9.0 cm R=6cm f= +3cm

Converging Lens S i = 4.29 cm S o =9.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/10cm = 1/ si S i = 4.29 cm M = - s i / s o = - 4.29 cm 10 cm M = -.429 Inverted Real Smaller

Converging Lens S i = 4.29 cm S o =9.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/9cm = 1/ si S i = 4.5 cm M = - s i / s o = - 4.5 cm 9.0 cm M = -.50 Inverted Real Smaller

Converging Lens S i = 4.29 cm S o =6.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/6cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Smaller

Converging Lens S i = 4.29 cm S o =6.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/6cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Same Size

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm - 1/6cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Same Size

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/4.5cm = 1/ si S i = 6.0 cm M = - s i / s o = - 6.0 cm 6.0 cm M = - 1.0 Inverted Real Same Size

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger

Converging Lens S i = 4.29 cm S o =3.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 Inverted Real Larger

Converging Lens S i = 4.29 cm S o =3.0 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/4.5cm = 1/ si S i = 9.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 No Image- Parallel RaysReal Larger

Converging Lens S i = 4.29 cm S o =2.1 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/2.1cm = 1/ si S i = -7.0 cm M = - s i / s o = - 9.0 cm 4.5 cm M = - 2.0 No Image- Parallel RaysReal Larger

Converging Lens S i = 4.29 cm S o =2.1 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/2.1cm = 1/ si S i = -7.0 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33 No Image- Parallel RaysReal Larger

Converging Lens S i = 4.29 cm S o =2.1 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/2.1cm = 1/ si S i = -7.0 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33 Upright

Converging Lens S i = 4.29 cm S o =2.1 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/2.1cm = 1/ si S i = -7.0 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33 Upright Virtual

Converging Lens S i = 4.29 cm S o =2.1 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/2.1cm = 1/ si S i = -7.0 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33 Upright Virtual Larger

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f=+3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/2.1cm = 1/ si S i = -7.0 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33 Upright Virtual Larger

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/3cm – 1/2.1cm = 1/ si S i = -7.0 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33 Upright Virtual Larger

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm Upright Virtual Larger 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) – 1/4.5cm = 1/ si S i = -7.0 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm Upright Virtual Larger 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) – 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-7.0 cm 2.1 cm M = +3.33

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm Upright Virtual Larger 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) – 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-1.8 cm 4.5 cm M =.40

Converging Lens S i = 4.29 cm S o =4.5 cm R=6cm f= - 3cm Upright Virtual Smaller 1/f = 1/s o + 1/s i 1/f-1/s o = 1/s i 1/(-3cm) – 1/4.5cm = 1/ si S i = -1.8 cm M = - s i / s o = - (-1.8 cm 4.5 cm M =.40

Compound Optical Instruement d o =___? h= ____ f 1 =___ cm f 2 = ___ cm 1.Measure d o, f 1,,f 2 h and draw rays to determine initial and final d i 2.Calculate initial and final d i positions 3.Measure final h and determine magnification by drawing and by calculations

Compound Microscope

S o =29 h=.67 f=15 S i =31 M=31/29 M=1.07 H=.75

Compound Microscope f e =26 S o =17

Compound Microscope

Compound Optical Instruement f=26 S o =17 h=.75 S i =-49 h = 2.0 M=49/17 M=2.9

Compound Microscope

Diffraction Path length differences produce constructive Interference if path length difference is a whole number multiples of the wavelength Destructive Interference will occur if path length difference is multiples of ½ of a wavelength

Single Slit Interference

Single Slit  max min

Single Slit  max min 

Single Slit  max Min 

Single Slit Diffraction 

 

  d Sin  = opp = m hyp d m = 0,1,2… for minima

Single Slit Diffraction   d Sin  = opp = m hyp d m = 0,1,2… for minima

Single Slit Diffraction   d Sin  = opp = m hyp d m = 1,2… for minima

Single Slit Diffraction   Sin  = opp = m hyp d m = 1,2… for minima

Single Slit  max min L = distance to screen

Single Slit  max min L = distance to screen xmxm X m distance To minima

Single Slit  max min Tan  = x m L xmxm X m distance To minima

Single Slit  max min Tan  = x m L xmxm X m distance To minima Sin  = m d

Single Slit  max min Tan  = x m L xmxm X m distance To minima Sin  = m d Tan  = sin 

Single Slit  max min Tan  = x m L xmxm X m distance To minima Sin  = m d Tan  = sin  X m = m L d

Young’s Double Slit Experiment

Young’s Double Slit Experiment Max

Young’s Double Slit Experiment Max 

Young’s Double Slit Experiment Max  

Young’s Double Slit Experiment Max   Sin  = m = xm d L Length (L) to screen

Young’s Double Slit Experiment Max   Sin  = m = xm d L Length (L) to screen xmxm

Young’s Double Slit Experiment Max   Sin  = m = x m = tan  d L = x m d m L Length (L) to screen xmxm

Multiple Slit Diffraction Sin  = m = x m d L = x m d m L 101101 m = 0, 1,2, 3 … max

Multiple Slit Diffraction Sin  = m = x m = tan  d L = x m d m L m L d 101101 m = 0, 1,2, 3 … max

Multiple Slit Diffraction Sin  = m = x m = tan  d L = x m d m L  x m m L d 101101 m = 0, 1,2, 3 … max

Single, Double, Multiple Slit Diffraction

Based on constructive and destructive interference

Single, Double, Multiple Slit Diffraction Based on constructive and destructive interference Caused by path length differences

Single, Double, Multiple Slit Diffraction Based on constructive and destructive interference Caused by path length differences Geometry based on sin  = m  x m =tan  d L

Single, Double, Multiple Slit Diffraction Based on constructive and destructive interference Caused by path length differences Geometry based on sin  = m  x m d L Single Slit m is for minima with broad central maxima Double / Multiple m is for maximum

Reflection-Interference, Newton’s Rings, Thin Film Interference Higher Index of Refraction Lower Index of Refraction

Reflection-Interference, Newton’s Rings, Thin Film Interference Higher Index of Refraction Lower Index of Refraction Relected ray experience a half wavelength phase change

Reflection-Interference, Newton’s Rings, Thin Film Interference

Higher Index of Refraction Lower Index of Refraction

Reflection-Interference, Newton’s Rings, Thin Film Interference Higher Index of Refraction Lower Index of Refraction No phase change occurs

Air Wedge Reflection-Interference Hair

Air Wedge Reflection-Interference

Air Glass

Phase change reflection

Air Wedge Reflection-Interference Phase change reflection – 180 0 – n air < n glass

Towards normal refraction

Air Wedge Reflection-Interference Towards normal refraction n air < n glass

No phase change reflection n glass >n air

Away from normal refraction

Air Wedge Reflection-Interference Away from normal refraction – n glass > n air

Away from normal refraction

Air Wedge Reflection-Interference Away from normal refraction n glass > n air speeds up

Phase change reflection

Air Wedge Reflection-Interference Phase change reflection n air < n glass

Towards normal refraction

Air Wedge Reflection-Interference Towards normal refraction n air < n glass

Air Wedge Reflection-Interference Towards normal

Air Wedge Reflection-Interference Away from normal refraction

Air Wedge Reflection-Interference Away from normal Refraction n glass > n air

Air Wedge Reflection-Interference Towards normal No Phase Change Away from normal Away from normal Phase Change Toward Normal Phase Change Away from normal

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change  l = d + ½  + d ½ + 2d = D l

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change If the path length of the light that is transmitted through the upper glass plate, then reflected off the air glass interference of the bottom plate with 180 degree phase reversal,then transmitted through the upper plate is multiples of ½ of a the path length of the light that is refracts through the upper glass plate, then reflects off the upper glass air interference without a phase change will interfer constructively.

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change  l = d + ½  + d ½ + 2d = D l d = distance between the plates

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change  l = d + ½  + d ½ + 2d = D l

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change  l = d + ½ + d ½ + 2d = D l

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change  l = d + ½  + d  l = ½ + 2d Constructive Interference = n

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change  l = d + ½  + d  l = ½ + 2d Constructive Interference =  l =m = ½ + 2d m=1/2 + 2 d

Air Wedge Reflection-Interference Towards normalNo Phase Change Away from normal Away from normal Phase Change Toward Normal Away from normal No Phase Change Phase Change  l = d + ½  + d  l = ½ + 2d Constructive Interference =  l =m = ½ + 2d 1/2 + 2 d

Thin Film Interference Antiflective coating with an index of refraction Greater than air but less than the glass lens n air =1.0 n thin film = 1.3 n glass = 1.7

Thin Film Interference

Effective refracted ray path length= thickness down * index of refraction because the wavelength decreases as it enters the higher index of refraction of the medium added to to thickness up * index of refraction added to ½ wavelength due to phase refersal. l effrr = nt + nt + ½ l effrr = 2nt+ ½ Reflected ray l effr = ½ Constructive inteference occurs at whole multiples of wavelength path length differences. Therefore in this case the refracted,reflected,refracted ray will show constructive interference if 2nt = m  t = m  approxiamately  2n Destructive interference occurs at ½ whole multiples of wavelength path length differences Therefore in this case the refracted,reflected,refracted ray will show destructive interference If 2nt = m  t=m  approxiamately 2 4n n =1.0 n thin film = 1.3

Thin Film Interference Antiflective coating with an index of refraction Greater than and the glass lens n air =1.0 n thin film = 1.6 n glass = 1.4

Thin Film Interference

Effective refracted ray path length= thickness down * index of refraction because the wavelength decreases as it enters the higher index of refraction of the medium added to to thickness up * index of refraction l effrr = nt + nt l effrr = 2nt Reflected ray l effr = ½ Constructive inteference occurs at whole multiples of wavelength path length differences. Therefore in this case the refracted,reflected,refracted ray will show constructive interference if 2nt = m  - ½  t = m +1/2  t = (m+1/2)  2n 2n Destructive interference occurs at ½ whole multiples of wavelength path length differences Therefore in this case the refracted,reflected,refracted ray will show destructive interference If 2nt = m  t = m +  2 4n 4n n =1.0 n thin film = 1.3

Thin Film Interference Effective refracted ray path length= thickness down * index of refraction because the wavelength decreases as it enters the higher index of refraction of the medium added to to thickness up * index of refraction added to ½ wavelength due to phase refersal. l effrr = nt + nt + ½ l effrr = 2nt+ ½ Reflected ray l effr = ½ Constructive inteference occurs at whole multiples of wavelength path length differences. Therefore in this case the refracted,reflected,refracted ray will show constructive interference if 2nt = m  t = m  2n Destructive interference occurs at ½ whole multiples of wavelength path length differences Therefore in this case the refracted,reflected,refracted ray will show destructive interference If 2nt = m  t=m 2 4n n =1.0 n thin film = 1.3

Thin film interference n 1 = air n 2 =1.33

Thin film interference n 1 =1.00 n 2 =1.33 n 3 =1.50

Thin film interference n 1 =1.00 n 2 =1.33 n 3 =1.50 m = 2 n t m = t (thickness of film) 2n

Thin film interference n 1 =1.00 n 2 =1.33 n 3 =1.50 m = 2 n t m = t (thickness of film) 2n If l was 4.8 x10 -7 m what would the miniumum thickness need to cause Constructive interference? If l was 4.8 x10 -7 m what would the miniumum thickness need to cause Destructive interference?

Summary Constructive interference – pathlength equals m Destructive interference – pathlength equal m 2 If n 1 n 3 or n 1 >n 2 <n 3 than t = (m+1/2)  constructive 2n If n 1 n 3 or n 1 >n 2 <n 3 than t = (m+1/2)  destructive 4n

Summary Constructive interference – pathlength equals m Destructive interference – pathlength equal m 2 If n 1 n 2 >n 3 than t = m  constructive 2n If n 1 n 2 >n 3 than t = m  destructive 4n

Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: Units Index of refraction of a medium equals the ratio.

Similar presentations

Presentation on theme: "Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: Units Index of refraction of a medium equals the ratio."— Presentation transcript:

Similar presentations

About project

Feedback

Log in

Auth with social network:

Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: Units Index of refraction of a medium equals the ratio.

Similar presentations

Presentation on theme: "Waves and optics formula Velocity equals the product of the frequency and the wavelength Formula: Units Index of refraction of a medium equals the ratio."— Presentation transcript:

Similar presentations

About project

Feedback