The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image is at a distance of 26 cm from the convex lens, calculate the new size of the image.

(1) 1.25 cm                             

(2) 2.5 cm

(3) 1.05 cm                             

(4) 2 cm

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

(a) 1.04°                     (b) 5°

(c) 0.96°                      (d) 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 :

(a) Are parallel to each other

(b) Are diverging

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

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

A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If $\mu$ is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is 

(a) ${\sin }^{-1}\left(\frac{1}{\mu }\right)$                             (b) ${\tan }^{-1}\left(\frac{1}{\mu }\right)$

(c) ${\sin }^{-1}\left(\frac{\mu -1}{\mu }\right)$                         (d) ${\cos }^{-1}\left(\frac{1}{\mu }\right)$

A plano-convex lens when silvered in the plane side behaves like a concave mirror of focal length 30 cm. However, when silvered on the convex side it behaves like a concave mirror of focal length 10 cm. Then the refractive index of its material will be 

(1) 3.0                               

(2) 2.0

(3) 2.5                               

(4) 1.5

A ray of light travels from an optically denser to rarer medium. The critical angle for the two media is C. The maximum possible deviation of the ray will be

(1) $\left(\frac{\mathrm{\pi }}{2}-C\right)$                         

(2) 2C

(3) $\mathrm{\pi }-2\mathrm{C}$                             

(4) $\mathrm{\pi }-\mathrm{C}$

A point object is moving on the principal axis of a concave mirror of focal length 24 cm towards the mirror. When it is at a distance of 60 cm from the mirror, its velocity is 9cm/sec. What is the velocity of the image at that instant?
           

(1) 5cm/sec towards the mirror

(2) 4cm/sec towards the mirror

(3) 4cm/sec away from the mirror

(4) 9cm/sec away from the mirror

Figure shows a cubical room ABCD with the wall CD as a plane mirror. Each side of the room is 3m. We place a camera at the midpoint of the wall AB. At what distance should the camera be focussed to photograph an object placed at A

(1) 1.5 m                                     

(2) 3 m

(3) 6 m                                         

(4) More than 6 m

If an object moves towards a plane mirror with a speed v at an angle $\theta$ to the perpendicular to the plane of the mirror, find the relative velocity between the object and the image

(a) v                                            (b) 2v

(c) 2v cos $\theta$                                    (d) 2v sin $\theta$