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Two vertical parallel mirrors A and B are separated by \( 10 \, \text{cm} \). A point object O is placed at a distance of \( 2 \, \text{cm} \) from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ________ \( \text{cm} \).

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is \( 12 \, \text{cm} \). When viewed from the opposite side, the apparent distance of the bubble is observed as \( 4 \, \text{cm} \). If the side of the ice cube is \( 24 \, \text{cm} \), the refractive index of the ice cube is:

An object is placed at a distance of \( 12 \, \text{cm} \) in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by \( 4 \, \text{cm} \) towards the stationary object. The distance by which the position of image would be shifted, will be:

In a medium the speed of light wave decrease to \( 0.2 \) times to its speed in free space the ratio of relative permittivity to the refractive index of the medium is \( x:1 \). The value of \( x \) is_____ :
(Given speed of light in free space = \( 3 \times 10^8 \, \text{m s}^{-1} \) and for the given medium \( \mu_r = 1 \) )

An object is placed on the principal axis of convex lens of focal length \( 10 \, \text{cm} \) as shown. A plane mirror is placed on the other side of lens at a distance of \( 20 \, \text{cm} \). The image produced by the plane mirror is \( 5 \, \text{cm} \) inside the mirror. The distance of the object from the lens is ______ \( \text{cm} \).

A convex lens of refractive index \( 1.5 \) and focal length \( 18 \, \text{cm} \) in air is immersed in water. The change in focal length of the lens will be ________ \( \text{cm} \). (Given refractive index of water = \( \frac{4}{3} \))

Two convex lenses of focal length \( 20\,\text{cm} \) each are placed coaxially with a separation of \( 60\,\text{cm} \) between them. The image of the distant object formed by the combination is at _____ \( \text{cm} \) from the first lens.

A biconvex lens of focal length \( 10 \, \text{cm} \) is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _________ \( \text{D} \).

As shown in the figure, a combination of thin plano concave lens and a thin plano convex lens is used to image an object at infinity. The radius of curvature of both the lenses is \( 30 \, \mathrm{cm} \) and refraction index of the material for both the lenses is \( 1.75 \). Both the lenses are placed at distance of \( 40 \, \mathrm{cm} \) from each other. Due to the combination, the image of the object is formed at distance \( x = \) ______ \( \mathrm{cm} \) from concave lens.

As shown in the figure, a plane mirror is fixed at a height of \( 50 \, \text{cm} \) from the bottom of tank containing water \( \left( \mu = \dfrac{4}{3} \right) .\) The height of water in the tank is \( 8 \, \text{cm} .\) A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror form the bottom of the tank is _________ \( \text{cm} .\)

A pole is vertically submerged in swimming pool, such that it gives a length of shadow \( 2.15 \, \text{m} \) within water when sunlight is incident at an angle of \( 30^\circ \) with the surface of water. If swimming pool is filled to a height of \( 1.5 \, \text{m} \), then the height of the pole above the water surface in centimeters is: \( (n_w = {4}/{3}) \)

A person has been using spectacles of power \( -1.0 \) dioptre for distant vision and a separate reading glass of power \( 2.0 \) dioptres. What is the least distance of distinct vision for this person?

The radius of curvature of each surface of a convex lens having refractive index \( 1.8 \) is \( 20 \, \text{cm} \). The lens is now immersed in a liquid of refractive index \( 1.5 \). The ratio of power of lens in air to its power in the liquid will be \( x : 1 \). The value of \( x \) is __________.

A fish rising vertically upward with a uniform velocity of \( 8 \, \text{m s}^{-1} \), observes that a bird is diving vertically downward towards the fish with the velocity of \( 12 \, \text{m s}^{-1} \). If the refractive index of water is \( \dfrac{4}{3} \), then the actual velocity of the diving bird to pick the fish, will be ________ \( \text{m s}^{-1} \).

A thin cylindrical rod of length \( 10\,\text{cm} \) is placed horizontally on the principle axis of a concave mirror of focal length \( 20\,\text{cm} \). The rod is placed in a such a way that mid point of the rod is at \( 40\,\text{cm} \) from the pole of mirror. The length of the image formed by the mirror will be \( \frac{x}{3}\,\text{cm} \). The value of \( x \) is ______.

Two objects A and B are placed at \( 15 \, \text{cm} \) and \( 25 \, \text{cm} \) from the pole in front of a concave mirror having radius of curvature \( 40 \, \text{cm} \). The distance between images formed by the mirror is:

As shown in the figure, three identical polaroids \( P_{1} \), \( P_{2} \) and \( P_{3} \) are placed one after another. The pass axis of \( P_{2} \) and \( P_{3} \) are inclined at angle of \( 60^\circ \) and \( 90^\circ \) with respect to axis of \( P_{1} \). The source \( S \) has an intensity of \( 256 \, \mathrm{W/m^{2}} \). The intensity of light at point \( O \) is ________ \( \mathrm{W/m^{2}} \).

A vessel of depth ‘\( d \)’ is half filled with oil of refractive index \( n_{1} \) and the other half is filled with water of refractive index \( n_{2} \). The apparent depth of this vessel when viewed from above will be:

The refractive index of a transparent liquid filled in an equilateral hollow prism is \( \sqrt{2} \). The angle of minimum deviation for the liquid will be _________\( ^\circ \).

Which of the following are true?
A. Speed of light in vacuum is dependent on the direction of propagation.
B. Speed of light in a medium is independent of the wavelength of light.
C. The speed of light is independent of the motion of the source.
D. The speed of light in a medium is independent of intensity.
Choose the correct answer from the options given below:

As shown in the figure, in Young’s double slit experiment, a thin plate of thickness \( t = 10 \, \mu \text{m} \) and refractive index \( \mu = 1.2 \) is inserted infront of slit \( S_{1} \). The experiment is conducted in air \( (\mu = 1) \) and uses a monochromatic light of wavelength \( \lambda = 500 \, \text{nm} \). Due to the insertion of the plate, central maxima is shifted by a distance of \( x \beta_{0} \), \( \beta_{0} \) is the fringe-width before the insertion of plate. The value of the \( x \) is _______.

When one light ray is reflected from a plane mirror with \( 30^\circ \) angle of reflection, the angle of deviation of the ray after reflection is:

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are:
A. Real
B. Erect
C. Smaller in size than object
D. Laterally inverted
Choose the most appropriate answer from the options given below:

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

When a beam of while light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called:

The critical angle for a denser-rarer interface is \( 45^\circ \). The speed of light in rarer medium is \( 3 \times 10^8 \, \text{m/s} \). The speed of light in the denser medium is:

A thin prism \( P_1 \) with an angle \( 6^\circ \) and made of glass of refractive index \( 1.54 \) is combined with another prism \( P_2 \) made from glass of refractive index \( 1.72 \) to produce dispersion without average deviation. The angle of prism \( P_2 \) is:

A point object, ‘O’ is placed in front of two thin symmetrical coaxial convex lenses \( L_1 \) and \( L_2 \) with focal length \( 24 \, \text{cm} \) and \( 9 \, \text{cm} \) respectively. The distance between two lenses is \( 10 \, \text{cm} \) and the object is placed \( 6 \, \text{cm} \) away from lens \( L_1 \) as shown in the figure. The distance between the object and the image formed by the system of two lenses is ______ \( \text{cm} \).

A ray of light is incident from air on a glass plate having thickness \( \sqrt{3} \, \text{cm} \) and refractive index \( \sqrt{2} \). The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ________ \( \times 10^{-2} \, \text{cm} \). (Given \( \sin 15^\circ = 0.26 \))

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index \( \frac{5}{3} \) is poured inside the bucket, the microscope have to be raised by \( 30 \, \text{cm} \) to focus the object again. The height of the liquid in the bucket is:

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JEE Main 2023 15th April Morning Shift

The refractive index of a transparent liquid filled in an equilateral hollow prism is \( \sqrt{2} \). The angle of minimum deviation for the liquid will be _________\( ^\circ \).