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 $\theta$

A thin prism having refracting angle ${10}^{°}$ is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be 

(a)$4^{°}$

(b)$6^{°}$

(c)$8^{°}$

(d)${10}^{°}$

Two identical glass $\left({\mu }_g=3/2\right)$ equi-convex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $\left({\mu }_w=4/3\right)$. The focal length of the combination is

(a)  $f/3$             (b) $f$

(c) $\frac{4f}{3}$               (d) $\frac{3f}{4}$

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use will be:

An astronomical telescope has an objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance of :
(1) 46.0 cm

(2) 50.0 cm  

(3) 54.0 cm

(4) 37.3 cm