Total Internal Reflection

In Fridays we discussed the critical angle, which is the measure of the angle of incidence when the angle of reflection is 90 degrees. If the angle of incidence is greater than the critical angle, total internal reflection occurs.

Total internal reflection only occurs when the following conditions are met:

• a light ray is in the more dense medium and approaching the less dense medium.
• the angle of incidence for the light ray is greater than the so-called critical angle.

when the angle of incidence in water reaches a certain critical value , the refracted ray lies along the boundary, having an angle of reflection of 90-degrees. this angle of incidence is know as the critical angle and is the largest angle of incidence for which refraction can still occur. for any angle of incidence greater than the critical angle, light will undergo total internal refraction.

The critical angle can be calculated from Snell's law by setting the refraction angle equal to 90-degrees.

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Refraction and Snell's law

In the last two days of class we learnt about the Absolute Index of Refraction, Snell's law and Finding Lateral Displacement.

- The speed of light in a material varies with the density of the material. The number tells us the density of a material is called the index of refraction.

- Changes in the light that are caused by the light entering different materials is called refraction.

n=c/v

n - absolute index of refraction

c - 3.0 x 10(to the power of 8), speed of light in vacuum

v - speed of light in a given material

The higher the index of refraction for a material/medium the more dense it is, therefore the slower the light travels.

Ex: calculate the speed of light in lucite.

n=c/v

v=?

c=3.0 x 10(to the power of eight.. no idea how to do that)

n=1.52

v=c/n v=3.0 x 10^8/ 1.52

v=1.97 x 10^8 m/s

Snell's law

n1 (sin 0i) = n2 (sin 0R)

n = index of refraction for each substance

0i = angle of incidence

0R = angle of refraction

sorry i couldn't keep going but we had valleyball practice and left early for Rosetown because the roads were bad

The Mathematics behind Curved Mirrors

Today in Physics 20 we started the class by viewing the a blog post from the previous day which we usually do. We also reviewed any questions and went over the difference between a converging mirror and a diverging mirror where Mr.Banow also brought out some examples to show the class.

For most of the period we individually worked on our "Curved Mirror Question Package" which had a variety of questions about curved mirrors (diverging, converging). some questions asked us to draw the rays of light and image on a converging or diverging mirror. some questioned asked what the image would look like when the object was placed in a different place in front of the converging/diverging mirror.

ex:

If the object is placed in front of a converging mirror at C, then the image will be inverted, real, the same size and at C.

Near the end of the package there where mathematical questions using the formulas we learned in class to find measurements such as:

hi: hight of the image

ho: hight of the object

di: the distance between the mirror and the image

do:the distance between the mirror and the object

M: Magnification (x)

In the last 5 minutes of class Mr.Banow showed us a pencil in a glass of water allowing us to describe what the pencil had looked like (broken, and larger) and also showing us how it looked upright (just larger)

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real world aplications of curved mirrors

we started class on Wednesday by thinking of different applications or curved mirrors

some examples are your right handed side mirror on your car, your head lights, flash lights and a disco ball

we also looked at two different types of telescopes

1 -light from distant stars enter the telescope tube in parallel rays

-these rays are reflected from a concave mirror to a diagonal plane mirror
-the diagonal plane mirror reflects the light to the eye piece which then focuses the light

-the larger the diameter of the mirror the brighter the light at the focus new telescopes can have diameters of up to 6m

2.cassegrain reflection telescope

-light rays reflect off a con crave mirror to a perpendicular plane mirror

-rays from the plane mirror proceed to and eye piece at the front which focuses the light.

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Curved Mirror Formulas

During this class we began working on a Practice sheet of curved mirror problems.
We used the following formulas:

M= hi/ ho = -di/do

1/di + 1/ do = 1/f

    Th Curved Mirror formula sheet is also useful.
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Locating Images on Curved Mirrors and the Curved Mirror Equation

Last day in class we looked at locating images on converging and diverging mirrors.

Converging Mirror

• the image is in front of the mirror and is between C and F
• the imge is real
• the image is inverted
• the image is smaller

Diverging Mirror

• the image is behind the mirror
• the image is virtual
• the image is upright
• the image is smaller

Note: Some rays near the edge of a spherical converging mirror may not be reflected right through the principle focus. This is called spherical aberration. This can be avoided by using parabolic mirrors. When drawing ray diagrmas we should "trust" the rays closer to the middle of the mirrors.

Today in class we looked at Curved Mirror Equations

M= hi/ho=-di/do 1/di+1/do=1/f

Sign Rules:

1. All distances are measured from the vertex of the mirror
2. Real images have a positive distance
3. Virtual images have a negative distance
4. Postitive Height and Magnification= Upright
5. Negative Height and Magnification= Inverted
6. Focal length of a diverging mirror is negative

Examples

1. A candle is located 30.0 cm from a converging mirror with a radius of curvature that is 10.0 cm

a) At what distance from the mirror will the image be formed?

• do=30.0cm
• f= 10.0/2= 5.0cm ( positive because the mirror is converging)
• di=?

• 1/di+1/do= 1/f
• 1/di+1/30.0 cm= 1/5.0cm
• 1/di=1/5.0 cm- 1/30.0 cm
• 1/di= 1/6
• di= 6.0 cm

b) If the candle is 4.0cm tall, how tall will it's image be?

• ho= 4.0 cm
• hi=?

• hi/ho=-di/do
• hi/4.0cm=-6.0cm/30.0cm
• hi=4.0cm(-6.0cm)/30.0 cm
• hi= -0.80 cm (inverted)

c)What are the characteristics of the image?

• in front (di positive) between C and F
• real (di positive)
• inverted (hi negative)
• smaller (hi

2. A pencil is located 30.cm from a diverging mirror with a focal length of 20.cm

a) where will the image be located?

• do=30. cm
• f=-20. cm (negative because the mirror is diverging)

• 1/di+1/do=1/f
• 1/di+ 1/30 cm= 1/-20 cm
• 1/di=1/-20 cm - 1/30 cm
• 1/di=-1/12
• di=-12 cm

b) If the pencil is 7.0 cm tall, how tall will it's image be?

• ho=7.0 cm
• hi= ?

• hi/ho= -di/do
• hi/7.0cm= -(-12cm)/3.0 cm
• hi= (12 cm)(7.0 cm)/30 cm
• hi= 2.8 cm

c) What is the magnification of the mirror?

• M=?
• M=hi/ho = 2.8cm/7.0 cm
• M= 0.40 x

d) what are the image's characteristics?

• behind mirror (di negative) between V and F
• virtual (di negative)
• upright (hi and M poitive)
• smaller (M<1)

Finding Images in Converging Mirrors

On Tuesday we started the next part of the light unit on curved mirrors. We learned that there are two types of curved mirrors, converging (concave) and diverging (convex) mirrors. There is a principal axis, and on it there is a focal point which we label F and a centre of curvature which we label C. At the point where the principal axis meets the mirror we label V for vertex.

 

We also learned the rules for locating images in curved mirrors. They are as follows:

1. An incident light ray that is parallel to the principal axis will reflect through the focus.

2. An incident light ray that travels through the focus will reflect back parallel to the principal axis.

3. An incident light ray that passes through the centre of curvature will reflect straight back along the same path.

We then looked at the rules for drawing ray diagrams for curved mirrors. They are:

1. Objects are drawn to the left of the mirror.

2. F and C must be measured to scale.

3. Every image has four characteristics:

*Position-relative to the mirror, F, C and V

*Type-real or virtual

*Attitude-upright or inverted

*Magnification-smaller, larger or the same size

Using these rules, we did some examples on how to draw these diagrams for concave mirrors.

http://www.physicsclassroom.com/mmedia/index.cfm#optics

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