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Reference: Physics for every day phenomena,

McGraw-hill.

You now know that light bends when going from medium 1 to medium 2. This is because, like the roman soldiers, the speed of the light depends on the medium. In a vacuum, light travels at 300, 000 km/s. However, the speed of light is smaller in glass or water. (you can imagine the stream of photons being slowed down by the matter that make up the medium.

Observe the figure. Light travels from medium 1 to medium 2.

How much light will bend, depends on both its speed in medium 1 and its speed in medium 2.

Source: physics of everyday phenomena, McGraw-Hill

animation

Index of refraction

If you are a science major (bio, phys,chem)

Do the problems without looking at the hints !

Only art majors can look, if they want.

The speed of light in a given medium is given by the formula: V = C/n

C is a constant. C is the speed of light is a vacuum (3 10⁸ m/s)

V is the speed in a given medium (glass, water, plastic ..)

n is the index of refraction. It is the ID of the medium.

n=1 for vacuum, n= 1.33 for water, n=1.6 for some kind of glass..

1) What is the speed of light in water, which has an index of refraction of 1.33?

(in m/s, in km/s). So V is what fraction of c ? (hint:V = k c. Find k, k is a fraction)

 

2) The speed of light is 1.9 10⁸m/s  in a clear plastic. Find the index of refraction of the plastic.

 

3) The speed of light in chloroform is 1.99 10⁸ m/s. What is its index of refraction?

 

4) A glass has an index of refraction of 1.5, find the speed of the light in it

 

5) The Sun is 1.5 10⁸km away from the Earth.

A) how long does it take for the light to reach us in minutes ?

B) If the space between Sun and Earth  were filled with water (n=1.33) how many more minutes would it take light to reach us?

Snell’s law (or Descartes law in Europe)

 

You now know that light bends at boundary. WE need a formula that give us the amount of bending. The amount of bending should depends on the speed of the light in the 2 media it travels through. It does/ The formula is called Snell’s law:

n1 sin(θ1) = n2 sin (θ2)

Source figure: physics of everyday phenomena, Mcgraw-hill

It does not matter if the light travels from medium1 to medium2 or from medium2 to medium2. Just reverse the arrows. Rays are reversible. This law was shown without trig by Snell and Descartes. Just using geometry.

 

 

6) A ray of light passes from water (n=1.33) to a sheet of flint glass (n=1.61), making an angle of incidence of 65 degrees. What is the angle of refraction.

Hint: collect data first. θ1 = 65, n1 = 1.33, n2 = 1.61, θ2 = ? . Use Snells formula to solve for  sin(θ2). Then solve for θ2 using sin ^–1 (inverse sine).

 

7) A block of crown glass (n=1.63) is immersed in an unknown liquid. A ray of light is measured to make an angle of incidence within the unknown liquid of 48 degrees as it approaches the glass. The angle in the glass is 36 degrees. What is the index of refraction of the liquid.

Hint: θ1=48, n1 = ? , n2=1.63, θ2=36. Use the formula and solve for n1.

 

8) From air (n=1), a light ray enters a piece of crown glass at an angle of 57 degrees and is refracted to 31 degrees inside the glass. What is the index of refraction of the glass ? (TRY WITHOUT HINTS, plEAEAEAEAEAEAEAse

Hint: θ1=57, n1=1, θ2=31, n2 = ?. Use the formula and solve for n2.

 

9) A ray of light is incident at an angle of 60 degrees upon the surface of crown glass (n=1.63) . What is the angle of refraction ?

Hint: n1=1, θ1=60, n2=1.63, θ2=  ? . Use the formula to solve for sin(θ2) and find θ2 using INV SIN.

 

10) advanced

A thick sheet of plastic , n=1.5, is used for the side of an aquarium tank. Light reflected from a fish in the water has an angle of incidence of 35 degrees. A what angle does the light enter the air (n=1).

(deal with 2 boundaries: water/plastic and then plastic/air)

 

11) extra credits

The speed of light in a clear plastic is 1.9 10⁸ m/s. A ray of light strikes the plastic at an angle of 22 degrees/ At what angle is the ray refracted

Trapped light

Observe the situation. A lamp is immerged in water. Rays strike the upper surface and bend away from the normal. Light travels from water (1.33) to air (1).

12)

A) n1 = 1.33, n2 =1

You know: 1.33 sin(θ1) = sin(θ2)

If θ1 is given, it is easy to find θ2 using your TI :

Enter Y1 = sin-1 (1.33 sin(X)) in the TI and use the TABLE key to  Fill the table: (first use TBLSET to ASK)

 

 

B) if θ1 =θcritical=  48.75346663, θ2 = ____

The ray is so much refracted, it travels along the surface. Can you use the formula for θ1=50 degrees ? If θ1 > 49, the ray does not _______ anymore. The ray is totally reflected and is trapped in the water. It is exactly what happens in optical fibres. Light is trapped inside glass and can carry information very fast.

 Θcritical (48.75.. ) is called the critical angle of incidence of water. Light undergoes total internal reflection if the angle of incidence is greater than the critical angle.

13) What is the critical angle of incidence of crown glass (n=1.63) ?

Hint: n1=1.63, θ1= ?, n2=1, θ2=90. solve for θ1.

 

14) what index of refraction must a transparant material have in order for the total internal reflection to take place at all agnles larger than 55 degrees ?

Hint: n1=?, θ1=55, n2 = 1, θ2 = 90. Solve for n1.

 

15) what is the critical angle of incidence of diamond (n=2.42) ? Can you see why a diamond sparkles ?

Hint: n1=2.42, n2=1, θ1= ?, θ2=90/ solve for θ1.

12) Here is a magic trick you can figure out using what you know from bending rays. Put a coin in a the bottom of an empty cup (not transparent) and position your eye so that the coin can’t be seen. See figure. How can you bring the coin into view without moving your head. (you can’t use a mirror). 

Applet to understand:

Total Reflection/refraction

Inside an optical fibre, light is trapped and can carry a huge amount of information (bits) over a very long distance. You can also use this technology to destroy an ulcer.

16) using your new knowledge, can you explain the formation of mirage ? Hint: The speed of light is faster in hot air than it is in cool air. (index of refraction smaller in hot air). Layer after layer , the air gets hotter near the ground. Also think total reflection. Waves bend away the fast layer.

17) In optical instruments like binocular or periscope, mirrors are not used anymore. We use prism of glass to reflect light. Here is how. (it has to do with total reflection at a boundary glass/air).

A) A prism of glass has a index of 1.5. Find its critical angle of incidence (above it, the ray is reflected).

 Hint: n1=1.5, n2=1, θ1= ?, θ2=90/ solve for θ1.

So if the angle of incidence > _________, light is reflected.

B) Using A Can you complete the figure by drawing the path followed by the incident ray ? The glass has an index of 1.5.

C) Can you see how to use 2 prisms to build a periscope ?

Complete the periscope by placing 2 prisms inside.

D) What do you think the person saw over the fence?

Hint: curiosity kills the cat (French citation)

CLICK HERE

12) A) From the diagram, calculate the angle of incidence and the angle of refraction

Hint: the angle of incidence: the angle between the normal and the incident ray. Refraction angle = angle between the normal and the refracted angle.

B) What is the refractive index of substance X.

 

13) advanced Here are some angles of incidences i with the corresponding angles of refraction r for glass. (table)

A) Plot a graph of angle i versus angle r.

You can use your TI. Use the statplot key.

Old school? Use a graph paper.

A) What angle of incidence will give an angle of refraction of 10.

With the TI find the best fit polynomial (3rd degree)

Y1. Then find intersection with Y2=10

A) What angle of refraction would you get for an angle of incidence of 36 ?

With TI use the table key. (ask option)