# Light enters at an angle of incidence in a transparent rod of refractive index n. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face what so ever be the value of angle of incidence  (1) $n>\sqrt{2}$                        (2) $n=1$ (3) $n=1.1$                        (4) $n=1.3$

Subtopic:  Total Internal Reflection |
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One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face, forms an image 10 cm behind the silvered face. The refractive index of the glass is [Consider that light ray returns back in the first medium]

(1) 0.4

(2) 0.8

(3) 1.5

(4) 1.6

Subtopic:  Refraction at Plane Surface |
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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

Subtopic:  Refraction at Plane Surface |
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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

Subtopic:  Refraction at Plane Surface |
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Two point light sources are $$24$$ cm apart. Where should a convex lens of focal length $$9$$ cm be put in between them from one source so that the images of both the sources are formed at the same place?
 1 $$6$$ cm 2 $$9$$ cm 3 $$12$$ cm 4 $$15$$ cm
Subtopic:  Lenses |
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There is an equi-convex glass lens with a radius of each face as $$R$$ and $$\mu_{ga}= \frac{3}{2}$$ and $$\mu_{wa} = \frac{4}{3}$$. If there is water in the object space and air in the image space, then the focal length is:
1. $$2R$$

2. $$R$$
3. $$\frac{3}{2}R$$
4. $$R^2$$

Subtopic:  Lens Makers' Formula |
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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. $$2^{\circ}$$

Subtopic:  Prisms |
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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.  ${\mathrm{sin}}^{-1}\left[\frac{{n}_{1}}{{n}_{2}}\mathrm{cos}\left({\mathrm{sin}}^{-1}\frac{{n}_{2}}{{n}_{1}}\right)\right]$

2.  ${\mathrm{sin}}^{-1}\left[{n}_{1}\mathrm{cos}\left({\mathrm{sin}}^{-1}\frac{1}{{n}_{2}}\right)\right]$

3.  ${\mathrm{sin}}^{-1}\left(\frac{{n}_{1}}{{n}_{2}}\right)$

4.  ${\mathrm{sin}}^{-1}\left(\frac{{n}_{2}}{{n}_{1}}\right)$

Subtopic:  Total Internal Reflection |
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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 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 $$B$$?

 1 $$1.5$$ 2 $$0.5$$ 3 $$1.3$$ 4 None of these
Subtopic:  Total Internal Reflection |
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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:

 1 zero 2 $$\alpha$$ 3 $$\sin^{-1}\left(\frac{1}{n}\right)$$ 4 $$2\sin^{-1}\left(\frac{1}{n}\right)$$
Subtopic:  Refraction at Plane Surface |
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