CONCEPTUAL PROBLEMS

1. Under what condition does prism produce the angle of minimum deviation?
2. A ray of light originated in air falls perpendicularly on the shorter face of a right angled isosceles (90^o – 45^o – 45^o) triangular glass prism of refractive index 1.5. Find the angle of deviation in this case in a diagram.
3. A glass prism is immersed in water. What happens to the value of angle of minimum deviation?
4. What do you understand by minimum deviation in the case of refraction through a prism? Plot a graph between angle of incidence and the deviation produced.
5. A 45^o – 45^o – 90^o glass prism is immersed in water. A ray of light is incident normally on one of its shorter faces. What is the minimum index of refraction that the prism must have if this ray is to be totally reflected?
6. State the factors on which the deviation produced by a prism depend.
7. Can you ever have situation in which light ray goes undeviated through a prism?
8. What are the advantages of total reflecting prism over plane mirror?

THEORY BASED PROBLEMS

9. Explain with necessary theory of measuring the refractive index of a prism by minimum deviation method.
   OR
   Discuss the phenomenon of refraction through prism. Derive an expression for the refractive index of the material of the prism in terms of the angle of minimum deviation.
10. Explain why a ray of light in air deviates while entering into a medium. Derive an expression for the refractive index of a glass prism if the ray suffers a condition of minimum deviation.
11. What is prism? Show that the deviation produced by a small angle prism is independent of the angle of incidence, provided the angle of incidence is small.
12. What is minimum deviation for prism? Prove that the refractive index of the prism is
    [latex]\mu = \frac{sin(\frac{A+\delta_m}{2})}{sin(\frac{A}{2})}[/latex]. Each symbol has its usual meaning.
13. Define angle of prism. Prove that the deviation produced by a small angle prism for small angle of incidence is independent of angle of incidence.
14. What is the cause of dispersion of light? Prove that the deviation produced by a small angle prism of incidence is independent of angle of incidence.

NUMERICAL PROBLEMS

1. A ray of light is refracted through a prism of angle 60^o. Find the angle of incidence so that the emergent ray just grazes in the second face. Refractive index of the material of the prism is 1.45. Ans: 24.2^o
2. A narrow beam of light incident normally on one face of an equilateral prism. The prism is surrounded by water, what is the angle between the direction of emergent beam in two cases. [latex](\mu_w = 1.33, \mu_g = 1.45)[/latex]. Ans: 49.29^o
3. A certain prism is found to produce a minimum deviation of 51^o while it produces a deviation of 62^o48’ for two values of angle of incidence, namely 40^o6’ and 82^o42’ respectively. Determine the refractive angle of prism, the angle of incidence at minimum deviation and the refractive index of the material of the prism. Ans: 60^o, 55.5^o, 1.64
4. A narrow beam of light incident normally on one face of an equilateral prism (refractive index 1.45) being surrounded by water (refractive index 1.33). At what angle the ray of light emerges out? Ans: 70.8^o
5. A glass prism of angle 60^o and refractive index 1.5 is immersed in water of refractive index 1.33. What will be the angle of minimum deviation for a ray of light passing symmetrically through the prism in water? Ans: 8.66^o
6. A glass prism of angle 72^o and index of refraction 1.66 is immersed in a liquid of refractive index 1.33. Find the angle of minimum deviation for a parallel beam of light passing through the prism. Ans: 22.38^o
7. A glass prism of angle of prism A and refractive index 1.5 produces the angle of minimum deviation equal to 40^o. Calculate the value of angle of prism. Ans: 62.8^o