Match the corresponding entries of Column 1 with Column 2. [Where m is the magnification produced by the mirror]

Column 1                         Column 2 
A. m=-2                     a. Convex mirror   
B. m=-1/2                  b. Concave mirror
C. m=+2                    c. Real image
D. m=+1/2                 d. Virtual Image

(1)A->a and c;B->a and d; C->a and b; D->c and d

(2)A->a and d; B->b and c; C->b and d; D-> b and c

(3)A->c and d; B->b and d;C->b and c;D->a and d

(4)A->b and c; B->b and c; C->b and d; D->a and d

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

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

A thin prism of angle $15°$ made of glass of refractive index ${\mathrm{\mu }}_1=1.5$ is combined with another prism of glass of refractive index ${\mathrm{\mu }}_2=1.75.$ The combination of the prism produces dispersion without deviation. The angle of the second prism should be 

(1) $7°$                                             

(2) $10°$

(3) $12°$                                             

(4) $5°$

A converging beam of rays is incident on a diverging lens. Having passed though the lens the rays intersect at a point 15cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5cm closer to the lens. The focal length of the lens is:

(1) -10cm                                   

(2) 20cm

(3) -30cm                                   

(4) 5cm

The speed of light in media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ is $1.5\times {10}^8 \mathrm{m}/\mathrm{s}$ and $2.0\times {10}^8 \mathrm{m}/\mathrm{s}$ respectively. A ray of light enters from medium ${\mathrm{M}}_1$ to ${\mathrm{M}}_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is

(1) equal to ${\sin }^{-1}\left(\frac{2}{3}\right)$

(2) equal to or less than ${\sin }^{-1}\left(\frac{3}{5}\right)$

(3) equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$

(4) less than ${\sin }^{-1}\left(\frac{2}{3}\right)$

A ray of light is incident on a $\mathrm{}$\(60^\circ\) prism at the minimum deviation position. The angle of refraction at the first face (ie, incident face) of the prism is:
1. zero
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

The refractive index of the material of a prism is \(\sqrt{2}\) and the angle of the prism is \(30^\circ.\) One of the two refracting surfaces of the prism is made a mirror inwards with a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is: