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Two identical equiconvex thin lenses each of focal lengths 20 cm, made of material of refractive index 1.5 are placed coaxially in contact as shown. Now, the space between them is filled with a liquid with a refractive index of 1.5. The equivalent power of this arrangement will be:

A ray of light falls on a transparent sphere as shown in the figure. If the final ray emerges from the sphere parallel to the horizontal diameter, then calculate the refractive index of the sphere. Consider that the sphere is kept in the air.
                                   
1.  $\sqrt{2}$ $$ 
2.  $\sqrt{3}$ $$
3.  $\sqrt{3/2}$ $$
4.  $\sqrt{4/3}$

A rod of glass ($\mu$ = 1.5) and of the square cross-section is bent into the shape as shown. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of a circular arc then for what maximum value of $\frac{d}{R}$, light entering the glass slab through surface A will emerge from the glass through B?
        

The slab of a refractive index material equal to 2 shown in the figure has a curved surface APB of a radius of curvature of 10 cm and a plane surface CD. On the left of APB is air and on the right of CD is water with refractive indices as given in the figure. An object O is placed at a distance of 15 cm from pole P as shown. The distance of the final image of O from P as viewed from the left is:
          

When a point object is seen by an observer through a glass slab, the image is
(1) seen nearer to the observer, but beyond the slab
(2) at the same distance from the observer as the object is 
(3) seen further from the observer
(4) seen near to the observer but between the slab and the observer

 The critical angle for light going from medium X into medium Y is $\theta$. The speed of light in medium X is $\nu$. The speed of light in medium Y is
(1) $\nu$(1 - cos $\theta$)
(2) $\nu$ / sin $\theta$
(3)  $\nu$ / cos $\theta$
(4)  $\nu$cos $\theta$

Monochromatic light of wavelength ${\lambda }_1$ travelling in a medium of refractive index $n_1$ enters a denser medium of refractive index $n_2$. The wavelength in the second medium is 
(1) ${\lambda }_1 (n_1/n_2)$                       (2) ${\lambda }_1 (n_2/n_1)$
(3) ${\lambda }_1(n_1-n_2)/n_2$                (4) ${\lambda }_1(n_2-n_1)/n_1$

Keeping the incident ray fixed, if a plane mirror is rotated through an angle $\theta$ about an axis lying in its plane, then the reflected ray turns through angle 
(1) 0              (2) 2$\theta$               (3) $\theta$/2              (4) 4$\theta$

A vessel of depth 2d cm is half filled with a liquid of refractive index ${\mu }_1$ and  the upper half with a liquid of refractive index ${\mu }_2$. The apparent depth of the vessel seen perpendicularly is
(1) $\left(\frac{{\mu }_1{\mu }_2}{{\mu }_1+{\mu }_2}\right)d$                     (2) $\left(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}\right)d$
(3) $\left(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}\right)2d$                 (4) $\left(\frac{1}{{\mu }_1{\mu }_2}\right)2d$

A bird in air looks at a fish vertically below it and inside water. $h_1$ is the height of the bird above the surface of water and $h_2$, the  depth of the fish below the surface of water. If refractive index of water with respect to air be $\mu$, then the distance of the fish as abserved by the bird is 
(1) $h_1+h_2$                    (2) $h_1+\frac{h_2}{\mu }$
(3) $\mu h_1+h_2$                  (4) $\mu h_1+\mu h_2$

In a concave mirror an object is placed at a distance $x_1$ from the focus and the image is formed at a distance $x_2$ from the focus. Then the focal length of the mirror is
(1) $x_1{x}_2$                        (2) $\sqrt{x_1{x}_2}$
(3) $\left(x_1+x_2\right)/2$            (4) $\sqrt{x_1/x_2}$

A double convex lens made of material of refractive index 1.5 and having a focal length of 10 cm is immersed in a liquid of refractive index 3.0. The lens will behave as
(1) converging lens of focal length 10 cm
(2) diverging lens of focal length 10 cm
(3) converging lens of focal length 10/3 cm
(4) converging lens of focal length 30 cm

A beam of light is converging towards a point I on a screen. A plane parallel plate of glass (thickness in the direction of beam t, refractive index $\mu$) is introduced in the path of the beam. The convergence point is shifted by
(1) t (1 - 1/$\mu$) away                     (2) t (1+1/$\mu$) away
(3) t (1 - 1/$\mu$) nearer                  (4) t (1+1/$\mu$) nearer

A thin lens has focal length f, and its aperture has diameter d. It forms an image of intensity I. Now, the central part of the aperture upto diameter d/2 is blocked by an opaque paper. The focal length and image intensity will change to
(1) f/2 and I/2                           (2) f and I/4   
(3) 3f/4 and I/2                         (4) f and 3I/4

An achromatic combination is formed using a convex and a concave lens in contact. The two lenses should have
(1) their powers equal
(2) their reflective indices equal
(3) their dispersive power equal
(4) the product of power and dispersive power of each lens should equal in magnitude but opposite in signs.

A parallel beam of monochromatic light is incident on one face of an equilateral prism, the angle of incident being 55$°$. The angle of emergence of the beam from the other face is 46$°$. The angle of minimum deviation is 
(1) < 41$°$                 (2) equal to 41$°$               (3) > 41$°$                    (4) $\ge 41°$

A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3) as shown in the figure. A light beam incident normally on the face AB is totally reflected to reach the face AC if

(1) sin $\theta$> 8/9                              (2) 2/3 < sin $\theta$ < 8/9
(3) $\sin \theta <2/3$                           (4) cos $\theta$ $\ge 8/9$

A ray is incident at an angle of incidence i on one surface of a prism of small angle A and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$, the angle of incidence i is nearly equal to
(1) A/$\mu$             (2) A/2$\mu$           (3) $\mu$A             (4) $\mu$A/2

In a telescope the magnification power of observer lens is $M_0$ and that of eyepiece is $M_e$, the total magnification power of telescope is
(1) $M_0$             (2) $M_e$          (3) $M_0$$\times$$M_e$              (4) $M_0$/$M_e$

The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and the eyepiece is found to be 20 cm. The focal length of lenses are 
(1) 18 cm, 2 cm            (2) 11 cm, 9 cm             
(3) 10 cm, 10 cm          (4) 15 cm, 5 cm