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) $\frac{3f}{4}$

An air bubble in a glass slab with refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and  3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is

(1) 8           

(2) 10

(3) 12         

(4) 16

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 

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 angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of deviation and refracting index of the material of the prism respectively are

(a)30°,$\sqrt{2}$

(b)45°,$\sqrt{2}$

(c)30°,$\frac{1}{\sqrt{2}}$

(d)45°,$\frac{1}{\sqrt{2}}$

The refracting angle of a prism is \(\text{A}\), and refractive index of the material of the prism is cot(A/2). The angle of minimum deviation is:

1. \(180^{\circ}-3\text{A}\)$$

2. \(180^{\circ}-2\text{A}\)

3. \(90^{\circ}-\text{A}\)

4. \(180^{\circ}+2\text{A}\)

In an astronomical telescope in normal adjustment a straight black line of length L is drawn on inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is l. The magnification of the telescope is:

(1)L/l+1

(2)L/l-1

(3)L+1/L-1

(4)L/l