Answer to Question #98669 in Optics for pinu

Question

a ray of light passes from air through a rectangular block of glass with parallel faces 6.5cm apart at an angle of incidence 35 degrees. calculate:
a) the angle of refraction
b) the lateral displacement

Answer 1

Calculation of angle of refraction and the lateral displacement

We need to find the angle of refraction and lateral displacement

Answer:

Angle of incident = i = $35^o$

Angle of refraction = r

Refractive index of Air = $n_1 = 1$

Refractive index of glass with respect to air = $n_2 = 1.65$

thickness of the glass = t = 6.5cm

a).

Formula of Snell's Law

$$\frac {sin i} {sin r} = \frac {n_2} {n_1}$$

Now plug the values in the formula,

$$\frac {sin \space 35^o} {sin r} = \frac {1.65} {1}$$

$$\frac {sin \space 35^o} {1.65} = \frac {sin r} {1}$$

$${sin r} = \frac {sin \space 35^o} {1.65} = \frac {0.5735} {1.65} = 0.3475$$

$$r = \arcsin (0.3457) = 20.33^o$$

(b).

Lateral displacement

$$=\frac {t \times sin \space (i - r)} {cos r}$$

Plug the values in the formula,

$$Lateral \space displacement = \frac {t \times sin \space (i - r)} {cos r} =\frac { 6.5 \times sin (35^o - 20.33^o)} {cos \space 20.33^o}$$

=

$$= \frac {6.5 \times 0.8613} {0.09} =62.2 cm$$