Question

A light ray is incident on a transparent sphere of refractive index root 2 at an angle of incidence 45 what is the deviation of a tiny fraction of the ray

Answer 1

from Snell's law,
$\mu_1sin\theta_1=\mu_2sin\theta_2$

$1.sin45^{\circ}=\sqrt{2}sinr$

$sinr=\frac{1}{2}=sin30^{\circ}$

r = 30° , see figure, r = r' = 30°

again apply Snell's law at second surface
$1sine=\sqrt{2}sinr$

$sine=\frac{1}{\sqrt{2}}=sin45^{\circ}$

e = 45°

now deviation at 1st surface
= i - r = 45° - 30° = 15°

deviation at 2nd surface
= e - r = 45° - 30° = 15°

total deviation = 15° + 15° = 30°

Answer 2

from Snell's law,

\mu_1sin\theta_1=\mu_2sin\theta_2μ

1

sinθ

1

=μ

2

sinθ

2

1.sin45^{\circ}=\sqrt{2}sinr1.sin45

∘

=

2

sinr

sinr=\frac{1}{2}=sin30^{\circ}sinr=

2

1

=sin30

∘

r = 30° , see figure, r = r' = 30°

again apply Snell's law at second surface

1sine=\sqrt{2}sinr1sine=

2

sinr

sine=\frac{1}{\sqrt{2}}=sin45^{\circ}sine=

2

1

=sin45

∘

e = 45°

now deviation at 1st surface

= i - r = 45° - 30° = 15°

deviation at 2nd surface

= e - r = 45° - 30° = 15°

total deviation = 15° + 15° = 30°