By Team Aakash Byju's | 16th December 2022

Applying Snell’s Law to Find the Angle of Total Deviation

A ray of light is incident on a glass sphere at an angle of incidence 60° as shown:

n

r = 60°, r’ = 60°, e =30°, δ        = 30°

A.

r = 60°, r’ = 30°, e = 30°, δ        = 60°

B.

r = 30°, r’ = 30°, e = 60°, δ        = 60°

C.

r = 60°, r’ = 60°, e = 60°, δ        = 60°

D.

total

total

total

total

Then the angles r, r’, e and the total deviation after two refractions are

Detailed Explanation

The correct answer is  option C. r = 30°, r’ = 30°,  e = 60°, δ       = 60°.

total

Arrow

Applying Snell’s Law to the refraction of the light incident with an angle of 60° with an angle of refraction r is given as

n sin60 = N sinr

sin r =

. . r =

1

(       )

√3

2

=

√3

sin r

sin 60 =

√3

2

. .

.

(                             )

1

√3

.

(       )

√3

2

=

1

2

30

o

1

2

(                          )

sin 30 =

. .

.

n

o

o

o

Next, apply Snell’s Law at the second surface with the angle of incidence r’ and angle of emergence e given as:

n sin e = N sin r

r = r  =

1

=

√3

sin r

30

o

. .

.

sin e

OA = OB, by similarity

n

sin e =√3 sin 30

. .

.

o

sin e =√3

(       )

√3

2

1

2

=

. .

.

e = 60

o

sin 60 =

√3

2

(                            )

So far we calculated that, r = 30°, r’ = 30° and e = 60°. Now, let us find the total deviation.

o

n

Firstly, find the deviation at both surfaces.

Deviation at the first surface =  i - r = 60 − 30  = 30°

Deviation at the second surface = i - r = 60 − 30  = 30°

o

o

o

o

n

Total deviation = deviation at first surface + deviation at second surface

δ        =30° + 30° = 60°

total

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