A ray of light incident on an equilateral prism at grazing incidence emerges from the prism at grazing emergence. The Refractive index of the prism is:

A prism having an apex angle \(4^{\circ}\) and refraction index \(1.5\) is located in front of a vertical plane mirror as shown in the figure. Through what total angle is the ray deviated after reflection from the mirror?

1. \(176^{\circ}\)
2. \(4^{\circ}\)
3. \(178^{\circ}\)
4. \(2^{\circ}\)

A glass prism $\left(\mu =1.5\right)$ is dipped in water $\left(\mu =4/3\right)$ as shown in figure. A light ray is incident normally on the surface AB. It reaches the surface BC after totally reflected, if

1. $\sin \theta <mspace\; width="1em"></mspace>\ge \raisebox{1ex}{$<mspace\; width="1em"></mspace>8$}\!\left/ \!\raisebox{-1ex}{$9$}\right.$                           
2. $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.<\sin \theta <mspace\; width="1em"></mspace><\raisebox{1ex}{$<mspace\; width="1em"></mspace>8$}\!\left/ \!\raisebox{-1ex}{$9$}\right.$
3. $\sin <mspace\; width="1em"></mspace>\theta <mspace\; width="1em"></mspace>\le <mspace\; width="1em"></mspace>\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$                           
4. It is not possible

An achromatic prism is made by crown glass prism $\left(A_c=19°\right)$ and flint glass prism

$\left(A_F=6°\right)$. If ${}_C\mu _v=1.5$ and ${}_F\mu _v=1.66$, then resultant deviation for red coloured ray will

be

1. 1.04°                     

2. 5°

3. 0.96°                     

4. 13.5°

An isosceles prism of angle 120° has a refractive index of 1.44. Two parallel

monochromatic rays enter the prism parallel to each other in air as shown. The rays

emerging from the opposite faces :

1. Are parallel to each other

2. Are diverging

3. Make an angle $2{\sin }^{-1}\left(0.72\right)$ with each other

4. Make an angle $2\left\{{\sin }^{-1}\left(0.72\right)-30°\right\}$ with each other

The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of deviation and refracting index of the material of the prism respectively are

1. 30°,$\sqrt{2}$

2. 45°,$\sqrt{2}$

3. 30°,$\frac{1}{\sqrt{2}}$

4. 45°,$\frac{1}{\sqrt{2}}$

The refracting angle of a prism is \(A\), and refractive index of the material of the prism is \(\cot{\left(\frac{A}{2}\right)}\). The angle of minimum deviation is:
1. \(180^{\circ}-3A\)
2. \(180^{\circ}-2A\)
3. \(90^{\circ}-A\)
4. \(180^{\circ}+2A\)

The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ of the prism is

1. 2sinA
 

2. 2cosA
 

3. 1/2cosA
 

4. tanA

A ray of light is incident at an angle of incidence, \(i\), on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is \(\mu\), the angle of incidence \(i\), is nearly equal to:
1. \(\mu A\)  
2. \(\dfrac{\mu A}{2}\) 
3. \(\frac{A}{\mu}\)
4. \(\frac{A}{2\mu}\)                                 

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index

1. lies between $\sqrt{2}$ and 1

2. lies between 2 and $\sqrt{2}$

3. is less than 1

4. is greater than 2