When a ray of light passes normally on the surface of separating the two media the angle of incidence is?

The reason that the light is not refracting is that it will take the path that will take the shortest time from through the medium. This is essentially what snell's law gives us. Since, we are looking at light at normal incidence there is no path that will take shorter time than to continue straight forward in the same medium.

You can think of it as a life guard who is trying to save a person drowning in a river. If the river is flowing and the life guard will run towards the person at an angle(on land) and he takes the current into account as he is faster on land than in the water. Thus, having different angles on land and in the water. If the water is still and the person needing help is straight out from the shore the life guard will run in a straight line to the shore and then swim straight out to rescue the person in the water.

Snell's law can be derived from Fermat's Principle which is the statement that the light will take the path that uses the least time. See the wikipedia article Snell's law for the derivation of the formula.

as mentioned by Aaron since the $\theta_1$ is zero, thus $\sin(\theta_1)=0$, $\theta_2$ needs to be zero for Snell's law to be satisfied. Below is snell's law: $$n_1\sin(\theta _1)=n_2\sin(\theta _2)$$

It is also possible to derive this directly form Maxwell's equations but that would be a boring and time consuming task.

Also note that if we are going from a medium with higher refractive index to a medium with lower refractive index we can get a situation where we will need $sin(\theta_2)$ to be greater than 1, this will result in a total internal reflection where no light will pass trough the interface.

Edited by Sim, Jen Moreau

When a beam of light strikes the boundary separating two transparent media such as air and water or glass, some of the light is reflected whereas the remaining portion enters the second medium and undergoes a change in direction as well as in velocity. This change of direction and velocity of light is called refraction of light.

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Consider a surface A'B' which separates two media. When a ray of light AO passes from one medium to the other, its direction changes along OC instead of straight line AB. Point 'O' is the point of incidence, NO'N is the normal to the surface A'B'. OA is the incident ray and OC is the refracted ray. The angle AON = Li and the angle CON' =Lr. From this discussion and experiment, it is clear that "when a light passes from a rare to a dense medium, the refracted ray bends towards the normal and when a ray of light passes from dense to a rare medium, the refracted ray bends away from normal as shown below (Note: glass is denser than water and water is denser than air).

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Snell’s law governs the imaging properties of lenses. Light rays passing through a lens are bent at both surfaces of the lens. With proper design of the curvatures of the surfaces, various focusing effects can be realized. For example, rays initially diverging from a point source of light can be redirected by a lens to converge at a point in space, forming a focused image. The optics of the human eye is centred around the focusing properties of the cornea and the crystalline lens. Light rays from distant objects pass through these two components and are focused into a sharp image on the light-sensitive retina. Other optical imaging systems range from simple single-lens applications, such as the magnifying glass, the eyeglass, and the contact lens, to complex configurations of multiple lenses. It is not unusual for a modern camera to have a half dozen or more separate lens elements, chosen to produce specific magnifications, minimize light losses via unwanted reflections, and minimize image distortion caused by lens aberrations.