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What is the position and nature of image formed by lens combination shown in figure? ( f1, f2 are focal lengths)

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Important Questions on Ray Optics

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A plano - convex lens (focal length f2 , refractive index μ2, radius of curvature R) fits exactly into a plano - concave lens (focal length f1, refractive index μ1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be:
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Formation of real image using a biconvex lens is shown below:

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If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen?
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A plano-convex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in fig-A If the same lens is instead silvered on the curved surface and illuminated from another side as in fig-B, it acts as an optical system of focal length 10 cm. The refractive index of the material of the lens is:

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A particle is oscillating on the x-axis with an amplitude 2 cm about the point x0=10 cm with a frequency. A concave mirror of focal length 5 cm is placed at the origin (see figure).

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Identify the correct statements?
(i) The image executes periodic motion.
(ii) The image executes non-periodic motion.
(iii) The turning points of the image are asymmetric with respect to the image of the point at X=10 cm.
(iv) The distance between the turning points of the oscillation of the image is 10021 cm.

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A ray of light is incident at an angle of 60 on one face of a prism of angle 30 . The emergent ray of light makes an angle of 30 with incident ray. The angle made by the emergent ray with second face of prism will be:
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A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is:
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Let the refractive index of a denser medium with respect to rarer medium be n12 and its critical angle be θC . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90o. Angle A is given by 
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In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is-