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 

1. ${\sin }^{-1}\left(\frac{1}{\mu }\right)$                            

2. ${\tan }^{-1}\left(\frac{1}{\mu }\right)$

3. ${\sin }^{-1}\left(\frac{\mu -1}{\mu }\right)$                        

4. ${\cos }^{-1}\left(\frac{1}{\mu }\right)$

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 room (cubical) is made of mirrors. An insect is moving along the diagonal on the floor

such that the velocity of image of insect on two adjacent wall mirrors is $10 cm{s}^{-1}$. The

velocity of image of insect in ceiling mirror is

1. 10 $cm{s}^{-1}$                           

2. 20 $cm{s}^{-1}$

3. $\frac{10}{\sqrt{2}}cm{s}^{-1}$                          

4. $10\sqrt{2}cm{s}^{-1}$

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

1. v                                           

2. 2v

3. 2v cos $\theta$                                    

4. 2v sin $\theta$

To an astronaut in a spaceship, the sky appears:

(1) Black                   

(2) White

(3) Green                 

(4) Blue

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle $\theta$, the spot of light is found to move through a distance y on the scale. The angle $\theta$ is given by 

(1) $\frac{y}{2x}$

(2) $\frac{y}{x}$

(3) $\frac{x}{2y}$

(4) $\frac{x}{y}$

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) $\frac{3f}{4}$