The refractive index of the material of a prism is \(\sqrt{2}\) and the angle of the prism is \(30^\circ.\) One of the two refracting surfaces of the prism is made a mirror inwards with a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:

An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of:

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 the light is found to move through a distance \(y\) on the scale. The angle \(\theta\) is given by:

A thin prism having refracting angle \(10^\circ\) is made of glass of a refractive index \(1.42\). This prism is combined with another thin prism of glass with a refractive index \(1.7\). This combination produces dispersion without deviation. The refracting angle of the second prism should be:
1. \(6^{\circ}\)
2. \(8^{\circ}\)
3. \(10^{\circ}\)
4. \(4^{\circ}\)

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

1.  $f/3$             
2. $f$
3. $\frac{4f}{3}$               
4. $\frac{3f}{4}$

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°,$\frac{1}{\sqrt{2}}$

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

A person can see objects clearly 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: