Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1:2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is

1.  1.1     

2.  1.2

3.  1.3

4.  1.4

The image of point P when viewed from the top of the slabs will be

(1)   2.0 cm above P

(2)   1.5 cm above P

(3)   2.0 cm below P

(4)   1 cm above P

2. \(R\)
3. \(\frac{3}{2}R\)
4. \(R^2\)

A prism having an apex angle \(4^{\circ}\) and refraction index \(1.5\) is located in front of a vertical plane mirror as shown in the figure. Through what total angle is the ray deviated after reflection from the mirror?

1. \(176^{\circ}\)
2. \(4^{\circ}\)
3. \(178^{\circ}\)
4. \(2^{\circ}\)

A rectangular glass slab ABCD, of refractive index $n_1$, is immersed in water of the refractive index $n_2\left(n_1>n_2\right)$. A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence ${\alpha }_{max}$, such that the ray comes out only from the other surface CD is given by

1.  ${\sin }^{-1}\left[\frac{n_1}{n_2}\cos \left({\sin }^{-1}\frac{n_2}{n_1}\right)\right]$           

2.  ${\sin }^{-1}\left[n_1\cos \left({\sin }^{-1}\frac{1}{n_2}\right)\right]$

3.  ${\sin }^{-1}\left(\frac{n_1}{n_2}\right)$                           

4.  ${\sin }^{-1}\left(\frac{n_2}{n_1}\right)$           

A rod of glass \((\mu = 1.5)\) and of the square cross-section is bent into the shape as shown. A parallel beam of light falls on the plane's flat surface \(A\) as shown in the figure. If \(d\) is the width of a side and \(R\) is the radius of a circular arc then for what maximum value of \(\frac{d}{R},\) light entering the glass slab through surface \(A\) will emerge from the glass through \(B?\)

A diverging beam of light from a point source \(S\) having divergence angle \(\alpha,\) falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is \(t\) and the refractive index \(n\), then the divergence angle of the emergent beam is:
   

A concave mirror is placed at the bottom of an empty tank with face upwards and axis vertical. When sunlight falls normally on the mirror, it is focused at distance of 32 cm from the mirror. If the tank is filled with water $\left(\mu =\frac{4}{3}\right)$ upto a height of 20 cm, then the sunlight will now get focussed at

(1) 16 cm above water level

(2) 9 cm above water level

(3) 24 cm below water level

(4) 9 cm below water level

The slab of a refractive index material equal to \(2\) shown in the figure has a curved surface \(APB\) of a radius of curvature of \(10~\text{cm}\) and a plane surface \(CD.\) On the left of \(APB\) is air and on the right of \(CD\) is water with refractive indices as given in the figure. An object \(O\) is placed at a distance of \(15~\text{cm}\) from the pole \(P\) as shown. The distance of the final image of \(O\) from \(P\) as viewed from the left is: