JEE Advanced Mi...

An opaque sphere of radius a is just immersed in a transparent liquid as shown in figure. A point source is placed on the vertical diameter of the sphere at a distance a/2 from the top of the sphere. One ray originating from the point source after refraction from the air liquid interface forms tangent to the sphere. The angle of refraction for that particular ray is 30º. The refractive index of the liquid is

A thin oil film of refractive index 1.2 floats on the surface of water (m = 4/3) When a light of wavelength l = 9.6 × 10^–7 m falls normally on the film from air, then it appears dark when seen normally. The minimum change in its thickness for which it will appear bright in normally reflected light by the same light is:

In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the slits then the variation of resultant intensity at mid-point of screen with 'µ' will be best represented by (µ ³ 1).[ Assume slits of equal width and there is no absorption by slab; mid point of screen is the point where waves interfere with zero phase difference in absence of slab]

Two blocks each of mass m lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB & CD of the two blocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces w.r.t. each other is:

A ray is incident on the first prism at an angle of incidence 53º as shown in the figure. The angle between side CA and B'A' for the net deviation by both the prisms to be double of the deviation produced by the first prism, will be :

Light of wavelength 4000 Å is incident at small angle on a prism of apex angle 4º. The prism has nv = 1.5 & n_r = 1.48. The angle of dispersion produced by the prism in this light is :

Two plane mirrors are joined together as shown in figure. Two point objects O₁ and O₂ are placed symmetrically such that AO₁ = AO₂. The image of the two objects is common if :

Monochromatic light rays parallel to x-axis strike a convex lens AB. If the lens oscillates such that AB tilts upto a small angle q (in radian) on either side of y-axis, then the amplitude of oscillation of image will be (f = focal length of the lens) :

A particle is moving towards a fixed convex mirror. The image also moves. If V_i = speed of image and V_O = speed of the object, then

The speed of light in the material of a plano convex lens is 2 × 108 m/s and its greatest thickness is 3 mm. If the aperture diameter of the lens in 6.0 cm then :