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A small bulb is placed at the bottom of a tank containing water to a depth of \( \sqrt{7} \, \text{m} \). The refractive index of water is \( \frac{4}{3} \). The area of the surface of water through which light from the bulb can emerge out is \( x \pi \, \text{m}^2 \). The value of \( x \) is ________.

The refracting angle of a prism is \( A \) and refractive index of the material of the prism is \( \cot(A/2) \). Then the angle of minimum deviation will be:

The speed of light in media ‘A’ and ‘B’ are \( 2.0 \times 10^{10} \, \text{cm/ s}^{} \) and \( 1.5 \times 10^{10} \, \text{cm/ s}^{} \) respectively. A ray of light enters from the medium \( B \) to \( A \) at an incident angle \( \theta \). If the ray suffers total internal reflection, then

Time taken by light to travel in two different materials A and B of refractive indices \( \mu_A \) and \( \mu_B \) of same thickness is \( t_1 \) & \( t_2 \) respectively. If \( t_2-t_1=5\times 10^{-10}\,s \) and the ratio of \( \mu_A \) to \( \mu_B \) is \( 1:2 \). Then, the thickness of material, in meter is: (Given \( v_A \) & \( v_B \) are velocities of light in A and B materials respectively.)

The difference of speed of light in the two media A and \( (v_A - v_B) \) is \( 2.6 \times 10^7 \, \text{m /s}^{} \). If the refractive index of medium B is \( 1.47 \), then the ratio of refractive index of medium B to medium A is: (Given : speed of light in vacuum \( c = 3 \times 10^8 \, \text{m s}^{-1} \) )

Light travels in two media \( M_1 \) and \( M_2 \) with speeds \( 1.5 \times 10^8 \, \text{ms}^{-1} \) and \( 2.0 \times 10^8 \, \text{ms}^{-1} \) respectively. The critical angle between them is:

A thin prism of angle \( 6^\circ \) and refractive index for yellow light \( (n_\gamma) \, 1.5 \) is combined with another prism of angle \( 5^\circ \) and \( n_\gamma = 1.55 \). The combination produces no dispersion. The net average deviation \( (\delta) \) produced by the combination is \( \left(\dfrac{1}{x}\right)^\circ \). The value of \( x \) is ______. 

A convex lens of focal length \( 20 \, \text{cm} \) is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is \( 10 \, \text{cm} \). A point object is placed on principal axis at a distance of \( 60 \, \text{cm} \) from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ______________ \( \text{cm} \).

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter \( 30 \, \text{cm} \) and refractive index \( 1.5 \). The distance from the centre of the globe at which the beam of light can converge is __________ \( \text{mm} \).

In the given figure, the face \( AC \) of the equilateral prism is immersed in a liquid of refractive index '\( n \)'. For incident angle \( 60^\circ \) at the side \( AC \), the refracted light beam just grazes along face \( AC \). The refractive index of the liquid \( n = \dfrac{\sqrt{x}}{4} \). The value of \( x \) is ________. (Given refractive index of glass \( = 1.5 \)). 

Light enters from air into a given medium at an angle of \( 45^\circ \) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \( 15^\circ \) from its original direction. The refractive index of the medium is :

Which of the following statement is correct?

The power of a lens (biconvex) is \( 1.25 \, \text{m}^{-1} \) in particular medium. Refractive index of the lens is \( 1.5 \) and radii of curvature are \( 20 \, \text{cm} \) and \( 40 \, \text{cm} \) respectively. The refractive index of surrounding medium:

An object ‘\( o \)’ is placed at a distance of \( 100 \, \text{cm} \) in front of a concave mirror of radius of curvature \( 200 \, \text{cm} \) as shown in the figure. The object starts moving towards the mirror at a speed \( 2 \, \text{cm/ s}\). The position of the image from the mirror after \( 10 \, \text{s} \) will be at __________ \( \text{cm} \).

In normal adjustment, for a refracting telescope, the distance between objective and eye piece is \( 30 \, \text{cm} \). The focal length of the objective, when the angular magnification of the telescope is \( 2 \), will be:

For an object placed at a distance \( 2.4 \, \text{m} \) from a lens, a sharp focused image is observed on a screen placed at a distance \( 12 \, \text{cm} \) form the lens. A glass plate of refractive index \( 1.5 \) and thickness \( 1 \, \text{cm} \) is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

A light ray is incident, at an incident angle \( \theta_1 \), on the system of two plane mirrors \( M_1 \) and \( M_2 \) having an inclination angle \( 75^\circ \) between them (as shown in figure). After reflecting from mirror \( M_1 \) it gets reflected back by the mirror \( M_2 \) with an angle of reflection \( 30^\circ \). The total deviation of the ray will be ________ degree.

A ray of light is incident at an angle of incidence \( 60^\circ \) on the glass slab of refractive index \( \sqrt{3} \). After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is \( 4\sqrt{3} \, \text{cm} \). The thickness of the glass slab is ________ \( \text{cm} \).

A convex lens has power \( P \). It is cut into two halves, along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

A light wave travelling linearly in a medium of dielectric constant \( 4 \), incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:

Two identical thin biconvex lenses of focal length \( 15 \, \text{cm} \) and refractive index \( 1.5 \) are in contact with each other. The space between the lenses is filled with a liquid of refractive index \( 1.25 \). The focal length of the combination is ________ \( \text{cm} \).