A parallel bean of light travelling in water (refractive index = 4/3) is refracted by a spherical bubble of radius 2 mm situation in water. Assuming the light rays to be paraxial. i. find the position of the image due to refraction at the first surface and the position of the final image, and ii. draw a ray diagram showing the positions of the images.

Figure shows a transparent hemisphere of radius 3.0 cm made of a material of refractive index 2.0. (a) A narrow beam of parallel rays is incident on the hemisphere as shown in the figure. Are the rays totally reflected at the plane surface ? (b) Find the image formed by the refraction at the first surface. (c) Find the image formed by the reflection or by the refraction at the plane surface. (d) Trace qualitatively the final rays as they come out of the hemisphere.

The refractive index of water is (4)/(3) and speed of light in air is 3xx10^(8)m//s . Find the speed of light in the water.

Light from a point source in air falls on a spherical glass surface (n = 1.5 and radius of curvature = 20 cm ). The distance of the light source from the glass surface is 100 cm. At what position the image is formed ?

A double convex lens made of glass of refractive index 1.5 has both radii of curvature 20 cm each. Find the focal length of the lens. If an object is placed at a distance of 15 cm from this lens, find the position of the image formed.

A beaker contains water up to a height h_1 and K oil above water up to another height h_2. Find the apparent shift in the position of the bottom of the beaker when viewed from above. Refractive index of water is mu_1 and that of K.oil is mu_2 .

A small object is placed at the centre of the bottom of a cylindrical vessel of radius 3 cm and height 4 cm filled completely with water. Consider the ray leaving the vessel through a corner. Suppose this ray and the ray along the axis of the vessel are used to trace the image. Find the apparent depth of the image and the ratio of real depth to the apparent depth under the assumptions taken. Refractive index -of water = 1-33.

An object is placed 21 cm in fron of a concave mirror of radius of curvature 20 cm.A glass slab of thicknes 3 cm and refractive index 1.5 is palced close to the mirror in the space between the object and the mirror. Find the position of the final image fromed. The distance of the nearer surface of the slab from the mirror is 10 cm.

A ball is kept at a height h above the surface of a heavy transparent sphere made of a material of refractive index The radius of the sphere is R. At t = 0, the ball is dropped to fall normally on the sphere. Find the speed of the image formed as a function of time for tlt sqrt((2h)/g) . Consider only the image by a single refraction.

The angle of a prism is A , One of its refracting surface is slivered . Light rays falling at an angle of incidence 2A on the first surface returns back through the same pathe after suffering reflection at the silvered surface. The refractive index mu of the prism is: