Internal Reflection Critical Angle

Introduction to laws of light reflection:

You can see an object only if light from it enters your eyes. Some objects such as the sun, electric lamps and candles make their own light. We call these luminous sources.

Most things you see do not make their own light but reflect it from a luminous source. They are non-luminous objects. The light source that works differently is the laser, invented in 1960.

Laws of reflection of light:

If we know how light behaves when it is reflected we can use a mirror to change the direction in which the light is traveling. This happens when a mirror is placed at the entrance of a concealed drive to give warning of approaching traffic.

An ordinary mirror is made by depositing a thin layer of silver on one side of a piece of glass and protecting it with paint. The silver – at the back of the glass – acts as the reflecting traffic.

From the below explanation we can understand the law of reflection of light.

Law of reflection of light explanation:

Let, we will see about the law of reflection of light.The terms used in connection with reflection are shown in the below figure. The vertical to the mirror at the peak where the incident ray strikes it is called the normal.

Note that the angle of occurrence i is the angle among the incident beam and the normal; similarly the angle of reflection r is the angle between the reflected ray and the normal.

(Source: Wikipedia)

The above figure shows the reflecting of light by a plane mirror, which is understood by the law of reflection.

The law of reflection states:

The angle of incidence equals the angle of reflection.

The incident beam, the replicate beam and the normal all lie in the equal plane. That is they can all be drawn on a flat sheet of paper.

By the above explanation we can understood the law of reflection of light.


If the ray is passed into the medium it is reflected away from the normal and it makes an angle. If the incidence of angle increases then the angle of reflection is also increases. If the denser medium has a certain ankle for incidence then the rarer medium has the refraction angle of 900.

Internal reflection critical angle

Critical angle:

In a denser medium for a certain angle of incidence there is a corresponding angle of refraction in rarer medium is 900. At this angle of incidence the angle of refraction is 900 which is known as critical angle. The critical angle is denoted by C.

Total internal reflection:

When an angle if incidence goes beyond the critical angle, the incident ray returns of denser medium because it is not refracted. This process is known as total internal reflection. That is in this total internal reflection the angle of incidence should be greater than the critical angle.

Internal reflection critical angle

Conditions for total internal reflection:

The ray have to flow from denser medium to rarer medium

The angle made by the incidence which is in denser medium should have the value higher than the critical angle for the pair of media.

Relation between refractive indices of media and critical angle:

Consider the refractive index of denser media is nd and refractive index for the rarer medium is nr.

Snell’s law:

According to the snell’s law the relation can be written as

‘(sin i)/(sin r)’='(n_r)/(n_d)’

For critical angle incidence i=C and r=900

‘(sin C)/(sin 90^0)’= ‘(n_r)/(n_d)’ ‘=>’ sin C = ‘1/(_rn_d)’

or sin C = ‘(n_r)/(n_d)’ = ‘1/(_rn_d)’

Here ‘_rn_d’ is the refractive index of the denser medium which is related to the rarer medium.

Consider the variable vr denotes the speed of light in rarer medium and vd is for denser medium .

Now the equation is sin C = ‘(v_d)/(v_r)’

Critical angles of some media relative to air:

The following table shows the critical angle for different mediums.

Substance Refractive index Critical angle
Water 1.33 48.750
Crown glass 1.52 41.14
Flint glass 1.65 37.31
Diamond 2.42 24.41

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