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A hemispherical paper weight contains a small flower on its axis of symmetry at a distance of 4 cm from its flat surface. Where is the flower appears to an observer when he looks at it along the axis of symmetry from the top? (Index of refraction of glass =1.5)

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Important Questions on Geometric Optics

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JEE Advanced
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A thin plano-convex lens acts like a concave mirror of radius of curvature 20 cm when its plane surface is silvered. The radius of curvature of the curved surface if index of refraction of its material is 1.5 will be
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JEE Advanced
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A ray of light, travelling in a medium of refractive index μ, is incident at an angle i on a composite transparent plate consisting of three plates of refractive indices μ1, μ2 and μ3. The ray emerges from the composite plate into a medium of refractive index μ4, at angle x. Then,
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JEE Advanced
IMPORTANT
The X-Z plane separates two media A and B with refractive indices μ1 and μ2 respectively. A ray of light travels from A and B. Its directions in the two media are given by the unit vectors r^A=ai^+bj^ and r^B=αi^+βj^ respectively, where i^ and j^ are unit vectors in the X and Y directions. Then,
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JEE Advanced
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Consider the situation as shown in figure. The point O is the centre. The light ray forms an angle of 60° with the normal.

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The normal makes an angle 60° with the horizontal and the mirror makes an angle 60° with the normal. The value of refractive index of that spherical portions so that light ray retraces its path is

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JEE Advanced
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The figure shows an equi-convex lens. What should be the condition on the refractive indices so that the lens becomes diverging?

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JEE Advanced
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An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object is kept at a distance of 6 cm from the same lens the image formed is virtual. If the size of the image formed are equal, the focal length of the lens will be
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JEE Advanced
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The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cc min-1 when water is being drained out at a constant rate. The amount of water drained in cc min-1 is (n1= refractive index of air, n2= refractive index of water)
MEDIUM
JEE Advanced
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A ray of light strikes a horizontal plane mirror at an angle of 45°. A second plane mirror is attached at an angle θ with it. If ray after reflection from second mirror runs parallel to the first mirror, then θ is