A cubic container is filled with a liquid whose refractive index increases linearly from top to bottom. Which of the following represents the path of a ray of light inside the liquid?
A clear transparent glass sphere ( μ = 1.5) of radius R is immersed in a liquid of refractive index 1.25. A parallel beam of light incident on it will converge to a point. The distance of this point from the centre of the sphere will be
A child in a toy car is moving towards a thin walled cubical glass container filled with water with a velocity of 3 cm/s, whereas fish is moving towards child with a velocity of 4 cm/s as shown in the figure. The wall behind the fish is silvered (Refractive index of water is μ = 4 / 3 and of glass wall is 1.5). Match the following Column – I Column – II A Velocity of child as observed by fish (p) Zero B Velocity of fish as observed by child (q) 6 cm/s C Velocity of image of fish by reflection from mirror as observed by child. (r) 8 cm/s D Velocity of image of child by reflection from mirror as observed by fish (s) 7 cm/s
A beaker of radius ? is filled with water (refractive index 4 3 ) up to a height ? as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed ? . This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is ℎ (ℎ≪?,ℎ≪?), as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature ?. Which of the following is/are correct? (g is the acceleration due to gravity)
Light is incident on a glass block as shown in figure. If θ 1 , is increased slightly, what happens to θ 2 ?
A fish is vertically below a flying bird moving vertically down toward water surface. The bird will appear to the fish to be
A fish looks upward at an unobstructed overcast sky. What total angle does the sky appear to subtend? (Take refractive index of water as 2 )
Let r and r’ denote the angles inside an equilateral prism, as usual, in degrees. Consider that during some time interval from t = 0 to t = t, r’ varies with time as r’ = 10 + t 2 . During this time, r will vary as (assume that r and r’ are in degree)
An object is placed at a distance of 25 cm from the pole of a convex mirror and a plane mirror is set at a distance 5 cm from convex mirror so that the virtual images formed by the two mirrors do not have any parallax. The focal length of the convex mirror is
A convex mirror and a concave mirror of radius 10 cm each are placed 15 cm apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in convex mirror, the position of the final image is
The image of an object placed on the principal axis of a concave mirror of focal length 12 cm is formed at a point which is 10 cm more distance from the mirror than the object. The magnification of the image is
A luminous point object is placed at O, whose image formed at I as shown in figure. Line AB is the optical axis. Which of the following statement is/are correct?
Two thin lens made of glass μ = 3 2 and water μ = 4 3 kept in contact with each other. An object is placed at point O. Assume all curved surfaces have equal radius. Match the following Columns: Column – I Column – II (A) (p) Final image of O will be real (B) (q) Final image of O will be Virtual (C) (r) Magnitude of focal length = 10 cm (D) (s) Magnitude of focal length = 15 cm (t) Magnitude of focal length = 25 cm
A parallel beam of light falls on a quarter cylinder of radius 9 cm, as shown in figure (A). Refractive index of the material of the cylinder is 3 . Maximum value of OP (in cm ), as shown in figure (B), so that rays don’t suffer TIR at the curved surface is (consider refractive index of surrounding medium equal to 1)
A ray of light is incident on a medium with angle of incidence i and refracted into a second medium with angle of refraction r. The graph of sin(i) vs. sin(r) is as shown in figure. Then, the velocity of light in the first medium is n times the velocity of light in the second medium. What should be the value of n?
A beam of light propagates through a medium 1 and falls onto another medium 2, at an angle α 1 , as shown in figure. After that, it propagates in medium 2 at an angle α 2 , as shown. The light’s wavelength in medium 1 is λ 1 What is the wavelength of light in medium2?
A circular beam of light of diameter d=2 cm falls on a plane surface of glass. The angle of incidence is 60° and refractive index of glass is μ =3/2. The diameter of the refracted beam is
One of the refracting surfaces of a prism of angle 30° is silvered. A ray of light incident at angle of 60° retraces its path. The refractive index of the material of prism is
A spherical mirror forms an image of magnification 3. The object distance, if focal length of mirror is 24 cm, may be
A plane glass mirror of thickness 3 cm of material of μ = 3/2 is silvered on the back surface. When a point object is placed 9 cm from the front surface of the mirror, then the position of the brightest image from the front surface is
The observer at O views two closely spaced spots on a vertical wall through an angled glass slab as shown in figure. As seen by observer, the spots appear
A ray of monochromatic light is incident on the refracting face of a prism (angle 75°). It passes through the prism and is incident on the other face at the critical angle. If the refractive index of the prism is 2 , then the angle of incidence on the first face of the prism is
An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?
A ray of light enters a rectangular glass slab of refractive index 3 at an angle of incidence 60°. It travels a distance of 5 cm inside the slab and emerges out of the slab. The perpendicular distance between the incident and the emergent rays is
A point object ‘O’ is at the centre of curvature of a concave mirror. The mirror starts to move at a speed u, in a direction perpendicular to the principal axis. Then, the initial velocity of the image is
In figure, ABC is the cross section of a right-angled prism and ACDE is the cross section of a glass slab. The value of θ so that light incident normally on the face AB does not cross the face AC is (given sin -1 (3/5) = 37°)
The refractive index of material of a prism of angles 45°, 45°, and 90° is 1.5. The path of the ray of light incident normally on the hypotenuse side is shown in
Refractive index of a prism is 7 3 and the angle of prism is 60°. The minimum angle of incidence of a ray that will be transmitted through the prism is
For a prism kept in air, it is found that for an angle of incidence 60 ° , the angle of refraction ‘ A ‘, angle of deviation ‘ δ ‘ and angle of emergence ‘e’ become equal. The minimum angle of incidence of a ray that will be transmitted through the prism is
A point object is placed at a distance of 25 cm from a convex lens. Its focal length is 22 cm. A glass slab of refractive index 1.5 is inserted between the lens and the object, then the image is formed at infinity. Find the thickness of the glass slab (in cm),
A plane mirror is rotating about ‘O’ with constant angular velocity 4 rad/sec in anticlockwise direction. A point ‘P’ is moving in a circle of radius 50 cm with constant speed 3 m/s in anticlockwise direction about point O. At a given instant as shown in figure, the angular velocity of image is (in rad/s) is
A parallel beam of light is incident from air at an angle ‘ α ‘ on the side PQ of a right angled triangular prism of refractive index n = 2 . Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45 0 . The angle ‘ θ ‘ of the prism in ‘ n ‘ times 3 0 . Find ‘n’?
In the arrangement shown in figure, image of light source O is obtained at the bottom of beaker containing water μ = 4 3 . The value of H is (given that O is 36cm from pole of lens and mirror is at 100 cm from lens)
Choose the correct statement(s)
Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n 1 surrounded by a medium of lower refractive index n 2 . The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n 1 and n 2 as shown in the figure. All rays with the angle of incidence i less than a particular value i m are confined in the medium of refractive index n 1 . The numerical aperture (NA) of the structure is defined as sin i m .
A ray of light is incident normally on one face of 30º – 60º – 90º prism of refractive index 5 3 , immersed in liquid of refractive index μ as shown in figure. Match List – I with List – II Column-I Column-II A) μ = 1 p) Ray will exit from prism at AC B) μ = 4 3 q) Ray will exit from prism at BC C) μ = 5 3 r) Ray will exit from prism making an angle sin − 1 5 9 with normal D) μ = 3 2 s) Ray will suffer a deviation δ such that 0 ≤ δ ≤ π 2 t) Ray will exit from prism making an angle of sin − 1 5 8 with normal
A block of mass 3 kg is attached with an ideal spring of spring constant 900 N/m. The other end of the spring is connected with a rigid wall. A fixed convex mirror of radius of curvature 120 cm is placed at a distance 110 cm from the block and the spring is in its natural length. The spring is extended by 100 cm and released. The speed of the image of block is v, when extension in the spring remains 50 cm. Find the value of ‘v’.
A plane mirror is rotating about ‘O’ with constant angular velocity 4 rad/sec in anticlockwise direction. A point ‘P’ is moving in a circle of radius 50 cm with constant speed 3 m/s in anticlockwise direction about point O. At a given instant as shown in figure, the angular velocity of image is (in rad/s) is
A thin biconvex lens of refractive index μ 2 and radii of curvatures R 1 and R 2 is placed between 2 medias of refractive index μ 1 and μ 3 as shown in figure: Column 1 Column 2 Column 3 (I) R 1 = 10 c m R 2 = 10 c m (i) μ 1 = 1 μ 3 = 3 / 2 (P) μ 2 = 1 (II) R 1 = 10 c m R 2 = 20 c m (ii) μ 1 = 1 μ 3 = 4 / 3 (Q) μ 2 = 4 / 3 (III) R 1 = 20 c m R 2 = 10 c m (iii) μ 1 = 3 / 2 μ 3 = 4 / 3 (R) μ 2 = 3 / 2 (IV) R 1 = 10 c m R 2 ∞ (iv) μ 1 = 4 / 3 μ 3 = 4 / 3 (S) μ 2 = 17 12 Which of the following configuration will not cause any angular deviation in the light beam passing through it?
An observer is standing at a point O, at a distance of 100 cm from a convex lens of focal length 50 cm. A plane mirror is placed behind the lens at a distance of 150 cm from lens. The magnitude of velocity of her own image as seen by the observer, at the moment when the mirror just starts moving with a velocity of 10 cm/s.
A triangular medium has varying refracting index n = n 0 + a x , where x is the distance (in cm) along x-axis from origin and n 0 = 4 3 . A ray is incident normally on face OA at the mid-point of OA. The range of a so that light does not escape through face AB when it falls first time on the face AB (OA = 4 cm, OB = 3 cm and AB = 5 cm): (Surrounding medium is air)
A plano convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28 cm. When its curved surface is silvered and plane not silvered, its equivalent to concave mirror of focal length 10 cm then the refractive index of material of lens is 2 9 × n . Calculate n
A point source of light is placed at a distance h below the surface of a large deep lake. The maximum area of the water surface through which light can escape directly from the water surface is π h 2 n 13 s q u a r e m e t e r then n is…… Refractive index of water = 4 3
A large square container with thin transparent vertical walls and filled with water (refractive index 4 3 ) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is
Two half convex lenses of focal lengths f 1 = 16 cm and f 2 = 21 cm respectively are placed such that their principal axes coincide. Both the lenses form image of a real point object O on a fixed screen as shown. The distance between object and screen is 100 cm. Then pick up the correct statement(s)
Remote objects are viewed through a converging lens with a focal length F=9 placed at a distance a=36 in front of the eye. Assume that the radius r of the pupil is approximately 1.5 mm. Choose the correct options.
A diver D is still under water μ = 4 3 at a depth d = 10 m. A bird is diving along line AB at a constant velocity in air. When the bird is exactly above the diver he sees it at a height of 50 m from himself and velocity of the bird appears to be inclined at 45° to the horizontal. At what distance (in m ) from the diver the bird actually hits the water surface.
Choose the correct mirror image of object as shown in the following figure.
Light travelling through three transparent substances follows the path shown in figure. Arrange the indices of refraction in order from smallest to largest. Note that total internal reflection does occur on the bottom surface of medium 2
What is the angle of incidence for an equilateral prism of refractive index 3 so that the ray is parallel to the base inside the prism?
The velocity of light in a medium is half its velocity in air. If a ray of light emerges from such a medium into air, the angle of incidence, at which it will be totally internally reflected, is
A candle is placed 20 cm from the surface of a convex mirror and a plane mirror is also placed so that the virtual images in the two mirrors coincide. If the plane mirror is 12 cm away from the object, what is the focal length of the convex mirror?
Consider the situation shown in figure. Water ( μ = 4/3) is filled in a beaker up to a height of 10 cm. A plane mirror is fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is
The image of point P when viewed from top of the slabs will shift by
Angle of minimum deviation is equal to the angle of prism A of an equilateral glass prism. The angle of incidence at which minimum deviation will be obtained is
A point source of light is placed in front of a plane mirror as shown in the figure. Determine the length of reflected path of light on the screen ∑ .
For the situations shown in figure, determine the angle by which the mirror should be rotated, so that the light ray will retrace its path after refraction through the prism and reflection from the mirror?
The critical angle for light going from medium X into medium Y is θ . The speed of light in medium X is ν . The speed of light in medium Y is
For a prism kept in air, it is found that for an angle of incidence 60°, the angle of refraction A, angle of deviation and angle of emergence e become equal. Then, the refractive index of the prism is
A real object is placed in front of a convex mirror (fixed). The object is moving toward the mirror. If ν 0 is the speed of object and v, is the speed of image, then
A concave mirror is placed on a horizontal table with its axis directed vertically upward. Let O be the pole of the mirror C its centre of curvature and F is the focus. A point object is placed at C.It has a real image, also located at C.If the mirror is now filled with water, the image will be
When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm. If the object is moved with a speed of 9 cm s-r the speed with which the image moves is
An object is approaching a fixed plane mirror with velocity 5 m s – 1 making an angle of 45 0 with the normal. The speed of image w.r.t. the mirror is
A ray of light from a denser medium strikes a rarer medium at art angle of incidence i. The reflected and refracted rays make an angle of π /2 with each other. If the angles of reflection and refraction are r and r’, then the critical angle will be
A ray of light travelling in glass ( μ = 3/2) is incident on a horizontal glass-air surface at the critical angle θ c If a thin layer of water ( μ = 4/3) is now poured on the glass-air surface, the angle at which the ray emerges into air at the water-air surface is
ACB is right-angled prism with other angles as 60° and 30°. Refractive index of the prism is 1.5. AB has thin layer of liquid on it as shown. Light falls normally on the face AC. For total internal reflections, maximum refractive index of the liquid is
A glass prism has refractive index 2 , and refracting angle 30°. One of the refracting surface of the prism is silvered. A beam of monochromatic light will retrace it path if its angle of incidence on the unsilvered refracting surface of the prism is
The image produced by a concave mirror is one-quarter the size of object. If the object is moved 5 cm closer to the mirror, the image will only be half the size of the object. The focal length of mirror is
A linear object AB is placed along the axis of a concave mirror. The object is moving towards the mirror with speed U. The speed of the image of the point A is 4U and the speed of the image of B is also 4U but in opposite direction. If the centre of the line AB is at a distanc e L from the mirror then find out the length of the object.
A mango tree is at the bank of a river and one of the branch of tree extends over the river. A tortoise lives in the river. A mango falls just on the tortoise. The acceleration of the mango falling from tree as it appears to the tortoise is (refractive index of water is 4/3 and the tortoise is stationary)
In the diagram shown, the lens is moving towards the object with a velocity V m/s and the object is also moving towards the lens with the same speed. What is speed of the image with respect to earth when the object is at a distance 2f from the lens? (f is the focal length):
A semi-cylinder made of transparent plastic has a refractive index n = 2 and a radius of R. There is a narrow incident light ray perpendicular to the flat side of the semi cylinder at d distance from the axis of symmetry.
The focal length of quartz lens for yellow color is 15.5 cm for which refractive index of quartz is 1.504. Find the focal length of same lens (in cm) for ultraviolet color for which refractive index is 1.434.
