(a) Explain the term critical angle.
(b) List two factors which determine the deviation of a ray of light by a triangular glass prism.
(c) The angle of refraction (r) of a ray of white light from air through a triangular glass prism of refractive index 1.5 is 29.0°. Calculate the angle through which the ray is least deviated.
(d) Study the ray diagram below and use it to answer the questions that follow.
Calculate the:
(i) values of angles P,Q and R;
(ii) refractive index n of the glass prism;
(iii) value of e;
(iv) total deviation D.
Explanation
Critical angle is the angle of incidence in the denser medium when the angle of refraction in the less dense medium is 90°.
(b) Deviation of a ray in a triangular prism is determined by the factors:
- Angle of incidence
- Refracting angle of the prism, and
- Refractive index of the prism material.
(c) A = 2r = 2 x 29 = 58\(^o\)
But n = \(\frac{sin \frac{1}{2} (A + Dm)}{sin \frac{1}{2}A} \)
sin \(\frac{1}{2}\)(A + Dm) = n sin A \(\frac{1}{2}\)A
58 + Dm = 93.32 - 58 = 35.32\(^o\)
(d) Angle P = 45° - 20° = 25°
But Angle Q = 180°- 60° = 120°
P +Q + R = 180°
Hence R = 180 - (P + Q) =180 - (25 + 120) = 35°
(ii) n = \(\frac{Sini}{sinP} = \frac{sin45^o}{sin45^o} = 1.673\)
(iii) n = \(\frac{sini}{sine} = \frac{sine}{sinR} = \frac{sinee^o}{sin35^o}\)
= 1.673 = \(\frac{sine}{sin35^o}\)
e = sin\(^{-1}\) (1.673 x sin 35\(^o\)) = 73.7\(^o\)
(iv) D = (i + e) - A = (45 + 73.3) - 60\(^o\)
= 58.3\(^o\)