(1) The face AC of a glass prism of angle 30º is silvered. A ray of light incident at an angle of 60º on face AB retraces its path on getting reflected from the silvered face AC. If the face AC is not silvered, the deviation that can be produced by the prism will be

(a) 0º

(b) 30º

(c) 45º

(d) 60º

(e)** **90º ** **

The deviation (*d*) produced by a prism is given by

*d* = *i*_{1} +* i*_{2} – *A* where *i*_{1} and * i*_{2} are respectively the angle of incidence and the angle of emergence and *A* is the angle of the prism. Here we have *i*_{1} = 60º,* i*_{2} = 0º (since the ray falling normally will proceed undeviated from the face AC if it is not silvered) and *A* = 60º.

Therefore, *d* = 30º.

(2) In the above question, what is the refractive index of the material of the prism?

(a) 1.732

(b) 1.652

(c) 1.667

(d) 1.5

(e) 1.414

In the triangle ADN angle AND is 60º since angle DAN = 30º and angle DNA = 90º. Therefore, the angle of refraction at D is 30º. The refractive index of the material of the lens (*n*) is given by

*n = *sin *i*_{1}/ sin*r*_{1} = sin 60º/ sin 30º = √3 = 1.732

(3) Two thin (small angled) prisms are combined to produce dispersion without deviation. One prism has angle 5º and refractive index 1.56. If the other prism has refractive index 1.7, what is its angle?

(a) 3º

(b) 4º

(c) 5º

(d) 6º

(e)** **7º** **

Since the deviation (*d*) produced by a *small angled* prism of angle *A *and refractive index *n* is given by

*d = *(*n *– 1)*A*, the condition for dispersion without deviation on combining two prisms of angles *A*_{1 }and *A*_{2} with refractive indices *n*_{1} and *n*_{2} respectively is

(*n*_{1}* *– 1)*A*_{1} = (*n*_{2}* *– 1)*A*_{2}

Therefore, 0.56×5 = 0.7×*A*_{2} so that *A*_{2} = 4º

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