Ray Optics and ...

Light travels in two media A and B with speeds $$1.8 \times { 10 }^{ 8 } m { s }^{ -1 }$$ and $$ 2.4 \times { 10 }^{ 8 } m { s }^{ -1 } $$ respectively. Then the critical angle between them is

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The mixture of a pure liquid and a solution in a long vertical column (i.e, horizontal dimensions <<vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical is deviated from its original path. Find the deviation in travelling a horizontal distance d << h, the height of the column. 

A glass prism has a right-triangular cross-section ABC, with $$\angle$$A$$=90^o$$. A ray of light parallel to the hypotenuse BC and incident on the side AB emerges grazing the side AC. Another ray, again parallel to the hypotenuse BC, incident on the side AC suffers total internal reflection at the side AB. Find the range of  the refractive index $$\mu$$ of the material of the prism?

A monochromatic light passes through a glass slab $$\left (\mu = \dfrac {3}{2}\right )$$ a thickness $$90\ cm$$ in time $$t_{1}$$. If it takes $$t_{2}$$ to travel the same distance through water $$\left (\mu = \dfrac {4}{3}\right )$$. The value of $$(t_{1} - t_{2})$$ is :

A ray of light is incident on a thick slab of glass of thickness t as shown in the figure. The emergent ray is parallel to the incident ray but displaced sideways by a distance d. if the angles are small then d is

Ocean appears blue due to _____________________.

In the given figure, the radius of curvature of a curved surface for both the piano-convex and plano-concave lens is 10 cm and refractive index for both is 1.5. The location of the final image after all the refractions through lenses is:

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A ray of light travelling in a medium of refractive index $$\mu$$ is incident at an angle $$\theta$$ on a composite transparent plate consisting of 50 plates of RI. $$1.0l\mu, \, 1.02\mu, \, 1.03\mu,\, ...., \, 1.50\mu.$$ The ray emerges from the composite plate into a medium of refractive index $$1 .6\mu$$ at  angle x. Then:

A point object O is placed at a distance of 20 cm in front of a equiconvex lens $$(^a\mu_g \, = \, 1.5)$$ of  focal length 10 cm. The lens is placed on a liquid of refractive index 2 as shown in the figure. An image will be formed at a distance h from a lens. The value of h is

A ray incident at a point at an angle of incidence of $${60}^{o}$$ enters a glass sphere of $$R.l.n=\sqrt 3$$ and is reflected and refracted at the further surface of the sphere. The angel between the reflected and refracted rays at this surface is