IITJEE Problems : Optics

Q 1. A concave mirror of radius of curvature 1m is placed at bottom of a tank of water. The mirror forms an image of the sun , when it is directly overhead. Calculate the distance of the images from the mirror for different depths, 80 cm and 40 cm of the water in the tank. (ans=50 cm , 47.5 cm)
Q 2. A pin is placed 10 cm in front of convex lens of focal length 20 cm made of material of refrective index 1.5. The surface of lens farther away from the pin is silvered and has a radius of curvature 22 cm. Determine the position of the final image. Is the image real or virtual.(Ans -11 cm)
Q 3. An object is placed 50 cm from the surface of a glass sphere of radius 12 cm along the diameter . Where will the final image be formed by reflection on both the surfaces? Refractive index of glass is 1.60 (Ans +9.5 cm)
Q 4. A bi-convex lens of radii of curvature 30.0 cm each is placed on the surface of water so that the lower surface is only immersed . An illuminated object 40 cm deep is observed vertically through the lens and water. Find the position of the image. Refractive index of air-glass=3/2 and of glass-air=4/3 . (ans -90 cm)
Q 5. Interference pattern is obtained with two coherent light sources of intensity ratio n. Show that in the interference pattern
(Imax-Imin)/(Imax+Imin)=2√n/(n+1)

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