91Ó°ÊÓ

The angle of Deviation. The incident angle uashown in Fig. is chosen so that the light passes symmetrically through the prism, which has refractive index nand apex angle A.

(a) Show that the angle of deviation d (the angle between the initial and final directions of the ray) is given by

$sin\frac{A+\mathrm{δ}}{2}=n\sin \frac{A}{2}$

(When the light passes through symmetrically, as shown, the angle of deviation is a minimum.)

(b) Use the result of part (a) to find the angle of deviation for a ray of light passing symmetrically through a prism having three equal angles 1A= 60.0_2and n= 1.52.

(c) A certain glass has a refractive index of 1.61 for red light (700 nm) and 1.66 for violet light (400 nm). If both colors pass through symmetrically, as described in part (a), and if A= 60.0_, find the difference between the angles of deviation for the two colors.

Step by step solution

01

Concept.

Law of refraction(Snell's law):

$n_1\sin {\mathrm{θ}}_1=n_2\sin {\mathrm{θ}}_2$

$n_1$=The index of refraction for material with incident light,

$n_2$=The index of refraction for material with refracted light

${\mathrm{θ}}_1$=angle of incidence,

${\mathrm{θ}}_2$=angle of refraction.

Note: the angle iS measured from the normal: a line drawn perpendicular to the surface at the point where the incident ray strikes the surface.

The Part of the light which continues into the second medium is transmitted rather than reflected, but the transmitted ray changes direction as it crosses the boundary. The transmission of light from one medium to another, but with a change in direction, is called refraction. The angles of the incidence and reflected light are described by (Snell's law) which is shown above.

02

Calculate part (a) of the problem.

03

Calculate part (b) of the problem.

$$\begin{gathered} \sin \left(\frac{A+a}{2}\right)=n\sin \frac{A}{2} \\ \frac{A+a}{2}=arc\sin \left(n\sin \frac{A}{2}\right) \\ a=2arc\sin \left(n\sin \frac{A}{2}\right)-A=2arc\sin \left(1.52×\sin \frac{60°}{2}\right)-60°=38.93° \end{gathered}$$

04

Calculate part (c) of the problem.

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