• A ray of light OA, starting from the object O, is incident on the surface PQ

normally, so it passes un deviated along the path AA'. Another ray OB, starting

along the object O, strikes the boundary surface PQ at B and suffers refraction.

Since, the ray travels from denser to rarer medium so it bends away from normal

N'BN drawn at the point of incidence B on the surface PQ and travels along BC

in air.

• When viewed by the eye, the ray BC appears to be coming from point I which is

the virtual image of O, obtained on producing A'A and CB backwards.

• Thus, any point seen from air will appear to be at I, which is lesser depth AI than

its actual depth AO.

• From the figure above; < 퐴푂퐵 = 푂퐵푵^′= 풊

• Also; < 퐵푰푨′ = 푪푩푵 = 풓

• Consider a right-angled triangle,

------ (i)

• Also, Consider a right-angled triangle,

• Now divide equation (i) into equation (ii)

• Thus; the refractive index from medium to air, by Snell’s law

• But the refractive index from air to medium is given by,

(Principle of reversibility of light)

• Therefore, the refractive index is given by

• The difference between real and apparent depth is known as vertical

displacement

Worked Examples

1. A fish at the bottom of a pond appears to be 1.2 m from the water surface. What

is the depth of the pond? The refractive index of water = 1.33 Solution;

Apparent depth, h = 1.2m, Depth of the pond, H =? 풂휼_풘= ퟏ. ퟑퟑ

From; refractive index,

2. A coin is placed at the bottom of a tall gas jar. When the jar is filled with paraffin

to a depth of 32.4 cm, the coin is apparently seen displaced 9.9 cm from the

bottom. What is the refractive index of paraffin?

Answer

Apparent depth = (32.4 – 9. 9) cm = 22.5 cm, Real depth (H) = 32.4 cm

Refractive Index in terms of Velocity of Light

 For a ray of light travelling from medium 1 to medium 2, refractive index is the

ratio of velocity of light in medium 1 to velocity of light in medium 2.

From Absolute Refractive index;

Thus;

Now; compare the two equations

Therefore;

• Whereby the ratio,

medium 1

is referred as the relative refractive index of medium 2 to

• For example, for a ray of light travelling from air to water

Worked Examples

1. The speed of light in air is 3.0 x 10⁸m/s. What is the speed of light in glass? Take

refractive index of glass = 1.5

Answer

Given:

= 1.5, C = 3.0 x 10⁸m/s

From:

2. What is the speed of light in a diamond? The refractive index of diamond

is 2.42 Given:

= 2.42, C = 3.0 x 10⁸m/s

From:

Critical Angle

• The critical angle is the angle of incidence where the angle of refraction is 90°.

The light must travel from an optically denser medium to an optically less dense

medium as in Figure below: When the angle of incidence is equal to the critical

angle, the angle of refraction is equal to ퟗퟎ^ퟎ.

• OR – Critical angle Is the angle of incidence beyond which rays of light passing

through a denser medium to the surface of a less dense medium are NO longer

refracted but totally reflected (see the figure below)

Whereby:

풄 = 풄풓풊풕풊풄풂풍 풂풏품풍풆

풓 = 풓풆풇풓풂풄풕풆풅 풂풏품풍풆 = ퟗퟎ^ퟎ

• If the angle of incidence is bigger than this critical angle, the refracted ray will

not emerge from the medium, but will be reflected back into the medium. This is

called total internal reflection.

Total Internal Reflection

 Total internal reflection Is the reflection due to the angle of incidence

exceeding the critical angle

 OR is a phenomenon that occurs when light travels from a more

optically dense medium to a less optically dense one. E g, glass to air

or water to air

 OR

is a phenomenon that occurs when a propagated wave strikes a medium

boundary at an angle larger than a particular critical angle with respect to the

normal to the surface

NB:

▪ The reflected ray goes back to denser medium

▪ When total internal reflection occurs, there is no refraction at all