1

and

…………..2

From the figure above; 푫 = 풂 + 풃

(sum of two opposite interior angles)

풃풖풕 … … . 풊 = 풂 + 풓 → 풂 = 풊 − 풓

풂풏풅

풓_ퟏ= 풃 + 풊_ퟏ→ 풃 = 풓_ퟏ− 풊_ퟏ

푡ℎ푒푛,

푫 = 풂 + 풃 = (풊 − 풓) + (풓_ퟏ− 풊_ퟏ)…………...(i)

Since: A and A₁is supplementary to each other

→ A + A₁= 180° …… (ii)

But:

r + i₁+ A₁= 180°…………………(iii) (sum of interior angles of a ∆)

 Compare equation (ii) and (iii)

r + i₁+ A₁= A + A₁

→ 푨 = 풓 + 풊_ퟏ→ 풓 = 푨 − 풊_ퟏ………(iv)

 Then substitute, equation (iv) into (i)

∴ 푻풉풆 풂풏품풍풆 풐풇 푫풆풗풊풂풕풊풐풏 풊풔 품풊풗풆풏 풃풚: 푫 = 풊+ 풓_ퟏ− 푨

The angle of deviation depends on

▪ The apical angle of the prism, A

▪ The Angle of incidence, i

▪ The refractive index of the glass prism.

NB: Angle of deviation decreases with an increase in the angle of incidence and

vice versa

Minimum Angle of Deviation, 푫_풎풊풏

• Is the deviation angle occurring when the emergent ray is refracted at an angle

equal to the angle of incidence.

• A prism is said to be in minimum deviation position when the angle of

incidence at the first surface is equal to the angle of emergence at the

second surface. In such a condition, the rays travel parallel to the base inside

the prism as seen from the figure below

and

Substitute:

and

In making

Thus;

From: Snell’s law

푫풎풊풏 + 푨

푺풊풏 (

)

풔풊풏풊

ퟐ

풂휼품 =

=

푨

풔풊풏풓

푺풊풏 ( )

ퟐ

 Consider the graph below shows the relationship between i and D, for

which the angle of deviation is obtained

Worked examples;

1. A monochromatic light is incident on an equilateral glass prism at an angle of

30⁰and emerges at an angle of 75⁰. What is the angle of deviation produced by

the prism?

0

ANS; given;

,

(for equilateral prism)

0

The angle of Deviation is given by:

2. The refractive index of the material of a prism with 60⁰angles for yellow light is

. At the position of minimum deviation, calculate the angle of;

(a) Minimum deviation

(b)Incidence; and

(c) Refraction

ANS; 풂휼_품= √ퟐ, A = 60⁰

(a) From;

 푫풎풊풏 + ퟔퟎ = ퟒퟓ × ퟐ = ퟗퟎ⁰

(b)From;

(Alternatively; you may use;

3. Light travelling through transparent oil enters into glass of refractive index 1.5. If

the refractive index of glass with respect to the oil is 1.25, what is the refractive

of the oil? ANS; 휼_품= ퟏ. ퟓ, 휼_품푶= ퟏ. ퟐퟓ, 휼_푶=?

From; Refractive index of glass with respect to oil,

Worked examples

1. How does the angle of minimum deviation produced by a prism change

with increase in

(i) the wavelength of incident light and

(ii) the refracting angle of the prism?

Answer

(i)

The angle of minimum deviation produced by a prism decreases with

increase in the wavelength of incident light.

(ii)

The angle of minimum deviation produced by a prism increases with

increase in the refracting angle of the prism.

2. A ray of light incident at an angle of incidence i passes through an equilateral

glass prism such that the refracted ray inside the prism is parallel to its base

and emerges at an angle of emergence r₁.

(i) How is the angle of emergence'r₁' related to the angle of

incidence 'i'

(ii) What can you say about the angle of deviation in such a

situation?

Answer

(i) Then angle of incidence i is equal to the angle of emergence

r₁. Hence, i = r₁

(ii) In this situation the angle of deviation is minimum

36° through an equilateral prism? Given that A= 60⁰[ANS; i = 48⁰S]

4. How does the deviation produced by a prism depend on

(i) the refractive index of its material, and

(ii) the wavelength of incident light

Answer

(i) For a given angle of incidence, the prism with a higher refractive index

produces greater deviation than the prism which has a lower refractive

index. For example — A flint glass prism produces more deviation than a

crown glass prism for same refracting angle since μflint > μcrown

(ii) The refractive index of a given transparent medium is different for the light of

different colours. It decreases with the increase in the wavelength of light.

Thus, the refractive index of the material of a prism for visible light is

maximum for the violet colour and minimum for the red colour.

Consequently, a given prism deviates violet light the most and red light the

least. (i.e.

δ violet > δ red since μviolet > μred)

7. A light ray falls at normal incidence on the first face of an equilateral prism

such that, the angle of incidence is 45⁰, and emerges from the second face by

making the same angle with the normal. What is the refractive index of the

material of the prism? [ANS; 1.4]

ANS; Given; A = 60⁰, 풊 = ퟒퟓ⁰, 푫 = ퟒퟓ + ퟒퟓ − ퟔퟎ = ퟑퟎ⁰

푫

(

푨

)

ퟑퟎ

(

ퟔퟎ

)

8. The angle of minimum deviation for a prism is 37⁰. If the angle of the prism is

60⁰, find the refractive index of the material of the prism. [ANS; 1.5]

Dispersion of white light

 When white light is passed through a glass prism it splits into its spectrum of

colours (in order violet, indigo, blue, green, yellow, orange and red) and

this process of white light splitting into its component colours is termed as

dispersion . The simplest way to explain dispersion is through dispersion in

the prism.

Activity

• We can perform an activity to show that white light consists of seven colours,

as follows: Take a glass prism. Allow a narrow beam of sunlight through a

small hole in the window of a dark room to fall on one face of the glass prism.

Let the light coming out of the other face of the prism fall on a white sheet of

paper or on a white wall (which will act as screen).

• A patch of seven colours will be formed on the sheet of white paper (or on

white wall). This shows that sunlight consists of seven colours.

• Please note that bulb light is also white light. So, bulb light coming through a

narrow slit can also be used to perform this activity.

• See the figure below:

The Rainbow

• Any light that gives a spectrum similar to that of sunlight is usually referred to as

white light. A rainbow is a natural spectrum appearing in the sky after a rain

shower on a sunny day. It is caused by the dispersion of sunlight by tiny water

droplets present in the atmosphere. A rainbow is always formed in a direction

opposite to that of the Sun.

• The water droplets act like small prisms. They refract and disperse the incident

sunlight, then reflect it internally, and finally refract it again when it comes out of

the raindrop. Due to the dispersion of light and internal reflection, different colors

reach the observer’s eye in distinct bands. You can also see a rainbow on a

sunny day when you look at the sky through a waterfall or through a water

fountain, with the Sun behind you.

Formation of a Rainbow

▪ A rainbow is caused by dispersion of sunlight by tiny water droplets, present in

the atmosphere. A rainbow is always formed in a direction opposite to that of

the Sun. The water droplets act like small prisms. They refract and disperse

the incident sunlight, then reflect it internally, and finally, refract it again when

it comes out of the raindrop. Due to the dispersion of light and internal

reflection, different colors reach the observer’s eye. (See the fig below)