TOTAL INTERNAL REFLECTION PART-2

A beam of light travels from water into a piece of diamond in the shape of a triangle, as shown in the diagram. Step-by-step, follow the beam until it emerges from the piece of diamond

(a) How fast is the light traveling inside the piece of diamond?
The speed can be calculated from the index of refraction:
(b) What is , the angle between the normal and the beam of light inside the diamond at the water-diamond interface?
A diagram helps for this. In fact, let's look at the complete diagram of the whole path, and use this for the rest of the questions. The angle we need can be found from Snell's law:
(c) The beam travels up to the air-diamond interface. What is , the angle between the normal and the beam of light inside the diamond at the air-diamond interface?
This is found using a bit of geometry. All you need to know is that the sum of the three angles inside a triangle is 180°. If is 24.9°, this means that the third angle in that triangle must be 25.1°. So:
(d) What is the critical angle for the diamond-air interface?

(e) What happens to the light at the diamond-air interface?
Because the angle of incidence (64.9°) is larger than the critical angle, the light is totally reflected internally.
(f) The light is reflected off the interface, obeying the law of reflection. It then strikes the diamond-water interface. What happens to it here?
Again, the place to start is by determining the angle of incidence
Because the angle of incidence is less than the critical angle, the beam will escape from the piece of diamond here. The angle of refraction can be found from Snell's law:

TOTAL INTERNAL REFLECTION

Total internal reflection is an optical phenomenon that occurs when a ray of light strikes a medium boundary at an angle larger than the critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary no light can pass through, so effectively all of the light is reflected. The critical angle is the angle of incidence above which the total internal reflection occurs.
When light crosses a boundary between materials with different refractive indices, the light beam will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the ray is closer to being parallel to the boundary) than the critical angle — the angle of incidence at which light is refracted such that it travels along the boundary — then the light will stop crossing the boundary altogether and instead be totally reflected back internally. This can only occur where light travels from a medium with a higher refractive index to one with a lower refractive index. For example, it will occur when passing from glass to air, but not when passing from air to glass.

REFRACTION

Refraction
When we talk about the speed of light, we're usually talking about the speed of light in a vacuum, indwhich is 3.00 x 108 m/s. When light travels through something else, such as glass, diamond, or plastic, it travels at a different speed. The speed of light in a given material is related to a quantity called the index of refraction, n, which is defined as the ratio of the speed of light in vacuum to the speed of light in the medium:
index of refraction : n = c / v
When light travels from one medium to another, the speed changes, as does the wavelength. The ex of refraction can also be stated in terms of wavelength:
Although the speed changes and wavelength changes, the frequency of the light will be constant. The frequency, wavelength, and speed are related by: c=frequency xwavelenght. The change in speed that occurs when light passes from one medium to another is responsible for the bending of light, or refraction, that takes place at an interface. If light is travelling from medium 1 into medium 2, and angles are measured from the normal to the interface, the angle of transmission of the light into the second medium is related to the angle of incidence by Snell's law : When light crosses an interface into a medium with a higher index of refraction, the light bends towards the normal. Conversely, light traveling across an interface from higher n to lower n will bend away from the normal. This has an interesting implication: at some angle, known as the critical angle, light travelling from a medium with higher n to a medium with lower n will be refracted at 90°; in other words, refracted along the interface. If the light hits the interface at any angle larger than this critical angle, it will not pass through to the second medium at all. Instead, all of it will be reflected back into the first medium, a process known as total internal reflection.