What if A is not given in the angle of deviation formula?

i + e - A

### Asked by gourimondal80 | 12th Nov, 2021, 08:09: PM

Expert Answer:

###
Figure shows the passage of light through a triangular prism ABC. The angles of incidence and refraction at the first face AB are i and r_{1},

while the angle of incidence (from glass to air) at the second face AC is r_{2} and the angle of refraction or emergence e. The angle between the

emergent ray RS and the direction of the incident ray PQ is called the angle of deviation, δ.
In the quadrilateral AQNR, two of the angles (at the vertices Q and R) are right angles.

Therefore, the sum of the other angles of the quadrilateral is 180º.

∠A + ∠QNR = 180º

From the triangle QNR, r_{1} + r_{2} + ∠QNR = 180º

Comparing these two equations, we get , r_{1} + r_{2} = A ..............................(1)

The total deviation δ is the sum of deviations at the two faces, δ = (i – r_{1} ) + (e – r_{2} ) ........................(2)

Hence , we get from eqn.(1) and eqn.(2) , δ = i + e – A ...........................(3)

------------------------------------------------------------------------------
To determine the angle of deviation δ , we use equation (3) .
From the known values of angle of incidence i , angle of emergence e and angle of prism A ,
we get angle of deviation δ from eqn.(3)
If angle of prism A is not known , then we use eqn.(2) . Eqn.(2) helps us to get angle of deviation δ from angle of incidence i,
angle of refraction r_{1} at incident surface , angle of emergence e and angle of incidence r_{2} at emergent surface .
Angle of refraction r_{1} is determined from Snell's law , sin(i) / sin(r_{1} ) = μ , where μ is refractive index of material of prism
Angle of incidence r_{2} is determined from Snell's law , sin(e) / sin(r_{2} ) = μ

_{1},

while the angle of incidence (from glass to air) at the second face AC is r

_{2}and the angle of refraction or emergence e. The angle between the

emergent ray RS and the direction of the incident ray PQ is called the angle of deviation, δ.

Therefore, the sum of the other angles of the quadrilateral is 180º.

∠A + ∠QNR = 180º

_{1}+ r

_{2}+ ∠QNR = 180º

Comparing these two equations, we get , r

_{1}+ r

_{2}= A ..............................(1)

The total deviation δ is the sum of deviations at the two faces, δ = (i – r

_{1}) + (e – r

_{2}) ........................(2)

_{1}at incident surface , angle of emergence e and angle of incidence r

_{2}at emergent surface .

_{1}is determined from Snell's law , sin(i) / sin(r

_{1}) = μ , where μ is refractive index of material of prism

_{2}is determined from Snell's law , sin(e) / sin(r

_{2}) = μ

### Answered by Thiyagarajan K | 12th Nov, 2021, 11:39: PM

## Application Videos

## Concept Videos

- what do you mean by refraction of light?
- how can you find the speed of the scooter that approches the mirror
- define the refractive index of benzene if the critical angle of it is 42
- The speed of light in a transparent medium is 0.6 times as that of its speed in vacuum. What is the refractive index of the medium? (a) 1.0 (b) 1.33 (c) 1.55 (d)1.66
- what is it
- Define critical angle for a pair of media.
- explain snell' law.
- Refraction of light class 10 simple defination
- The refractive index of water is 4/3 and that of glass is 3/2 . The ratio of speed of light in water to the glass is

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change