A concave mirror of radius 40 cm lies on a horizontla tale and wateis filled in it up t a heightof 5.00 cm. A small dust particle floats on the water surface at a point P vertically above tge pointof contact of the miror with the table. Locate the image of the dust particle as seen from a point directly above it. tEh refractie index of water is 1.33.

One side of radius of curvature R_2=120 cm of a convexo-convex lens of material of refractive index mu=1.5 and focal length f_1=40 cm is slivered. It is placed on a horizontal surface with silvered surface in contact with it. Another convex lens of focal length f_2=20 cm is fixed coaxially d=10 cm above the first lens. A luminous point object O on the axis gives rise to an image coincide with it. Find its height above the upper lens.

A vessel is fully filled with liquid having refreactive index 5/3 . At the bottom of the vessel a point-like source of light is kept. An observer looks at the source of light from the top. Now, an opaque circular disc is kept on the surface of the water in such a way that its centre just rests above the light source. Now liquid is taken out from the bottom gradually. Calculate the maximum height ofthe liquid to be kept so that light source cannot be seen from outside. (Radius of the disc is 1 cm.)

A small pin fixed on a table top is viewed from above from a distance of 50cm. By what distance would the pin appear to be raised if it is viewed from the same point through a 15cm thick glass slab held parallel to the table? Refractive index of glass = 1.5. Does the answer depend on the location of the slab?

Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away from her and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, how much string does she have out (see the given figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

A point object lies 30 cm above water on the axis of a convex mirror of focal length 40 cm lying 20 cm below water surface. Consider two images. (i) Image formed by the partial reflection from water surface. (ii) Image formed by refraction from water surface followed by reflection from mirror and again refraction out of the water surface. find the distance between these two images.