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In a long glass tube, mixture of two liquids \( A \) and \( B \) with refractive indices \( 1.3 \) and \( 1.4 \) respectively, forms a convex refractive meniscus towards \( A \). If an object placed at \( 13 \, \text{cm} \) from the vertex of the meniscus in \( A \) forms an image with a magnification of \( '-2 '\) then the radius of curvature of meniscus is:

A bi-convex lens has radius of curvature of both the surfaces same as \( \frac{1}{6} \, \text{cm} \). If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides \( (R_1 \neq R_2) \), without any change in lens power then possible combination of \( R_1 \) and \( R_2 \) is:

A plano-convex lens having radius of curvature of first surface \( 2 \, \text{cm} \) exhibits focal length of \( f_{1} \) in air. Another plano-convex lens with first surface radius of curvature \( 3 \, \text{cm} \) has focal length of \( f_{2} \) when it is immersed in a liquid of refractive index \( 1.2 \). If both the lenses are made of same glass of refractive index \( 1.5 \), the ratio of \( f_{1} \) and \( f_{2} \) will be:

Two concave refracting surfaces of equal radii of curvature and refractive index \(1.5\) face each other in air as shown in figure. A point object \(O\) is place midway, between \(P\) and \(B\). The separation between the images of \(O\), formed by each refracting surface is:

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \( R = 2 \, \text{m} \). Another car approaches him from behind with a uniform speed of \( 90 \, \text{km} / \text{hr} \). When the car is at a distance of \( 24 \, \text{m} \) from his, the magnitude of the acceleration of the image of the car in the side view mirror is \(' a' \). The value of \( 100a \) is ______ \( \text{m} / \text{s}^2 \).

Given a thin convex lens (refractive index \( \mu_2 \)), kept in a liquid (refractive index \( \mu_1 \), \( \mu_1 < \mu_2 \)) having radii of curvatures \( |R_1| \) and \( |R_2| \). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of \( 12 \, \text{cm} \), at same distance of \( 18 \, \text{cm} \) from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

A concave mirror of focal length \( f \) in air is dipped in a liquid of refractive index \( \mu \). Its focal length in the liquid will be:

Given is a thin convex lens of glass (refractive index \( \mu \)) and each side having radius of curvature \( R \). One side is polished for complete reflection. At what distance form the lens, an object be placed on the optic axis so that the image gets formed on the object itself?

Given below are two statements: one labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): Refractive index of glass is higher than that of air.
Reason (R): Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.
In the light of the above statements, choose most appropriate answer from the options given below:

A slanted object \( AB \) is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:

A spherical surface separates two media of refractive indices \( 1 \) and \( 1.5 \) as shown in figure. Distance of the image of an object \( 'O' \), is: (\( C \) is the center of curvature of the spherical surface and \( R \) is the radius of curvature)

In an experiment with a closed organ pipe, it is filled with water by \( \left( \dfrac{1}{5} \right) \)th of its volume. The frequency of the fundamental node will change by:

Two thin convex lenses of focal lengths \( 30 \, \text{cm} \) and \( 10 \, \text{cm} \) are placed coaxially, \( 10 \, \text{cm} \) apart. The power of this combination is:

A container contains a liquid with refractive index of \( 1.2 \) up to a height of \( 60 \, \text{cm} \) and another liquid having refractive index \( 1.6 \) is added to height \( H \) above first liquid. If viewed from above, the apparent shift in the position of bottom of container is \( 40 \, \text{cm} \). The value of \( H \) is __________ \( \text{cm} \). (Consider liquids are immiscible)

A spherical surface of radius of curvature \( R \), separates air from glass (refractive index \( = 1.5 \)). The centre of curvature is in the glass medium. A point object ‘O’ placed in air on the optic axis of the surface, so that its real image is formed at ‘I’ inside glass. The line \( OI \) intersects the spherical surface at \( P \) and \( PO = PI \). The distance \( PO \) equals to:

The radii of curvature for a thin convex lens are \( 10 \, \text{cm} \) and \( 15 \, \text{cm} \) respectively. The focal length of the lens is \( 12 \, \text{cm} \). The refractive index of the lens material is:

A finite size object is placed normal to the principal axis at a distance of \( 30 \, \text{cm} \) from a convex mirror of focal length \( 30 \, \text{cm} \). A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:

A thin prism \( P_{1} \) with angle \( 4^\circ \) made of glass having refractive index \( 1.54 \), is combined with another thin prism \( P_{2} \) made of glass having refractive index \( 1.72 \) to get dispersion without deviation. The angle of the prism \( P_{2} \) in degrees is:

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to \( |R_1| \) and \( |R_2| \), i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is:

What is the relative decrease in focal length of a lens for an increase in optical power by \( 0.1 \, \text{D} \) from \( 2.5 \, \text{D} \)? (\( \text{‘D’} \) stands for dioptre)

A convex lens of focal length \( 30 \, \text{cm} \) is placed in contact with a concave lens of focal length \( 20 \, \text{cm} \). An object is placed at \( 20 \, \text{cm} \) to the left of this lens system. The distance of the image from the lens in \( \text{cm} \) is ______.

Two light beams fall on a transparent material block at point \( 1 \) and \( 2 \) with angle \( \theta_{1} \) and \( \theta_{2} \), respectively, as shown in figure. After refraction, the beams intersect at point \( 3 \) which is exactly on the interface at other end of the block.
Given: the distance between \( 1 \) and \( 2 \), \( d = 4\sqrt{3} \, \text{cm} \) and \( \theta_{1} = \theta_{2} = \cos^{-1}\!\left(\frac{n_{2}}{2 n_{1}}\right) \), where refractive index of the block \( n_{2} > \) refractive index of the outside medium \( n_{1} \), then the thickness of the block is __________ cm.

Light from a point source in air falls on a spherical glass surface (refractive index, \( \mu = 1.5 \) and radius of curvature = \( 50 \, \text{cm} \)). The image is formed at a distance of \( 200 \, \text{cm} \) from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is ________ \( \text{m} \),

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to \( 60^\circ \). The refractive index of the prism material is \( \sqrt{2} \). The angle of incidence (in degrees) is __________.

A mirror is used to produce an image with magnification of \( \frac{1}{4} \). If the distance between object and its image is \( 40 \, \text{cm} \), then the focal length of the mirror is ______.

A thin plano convex lens made of glass of refractive index \( 1.5 \) is immersed in a liquid of refractive index \( 1.2 \). When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length \( 0.2 \, \text{m} \). The radius of curvature of the curved surface of the lens is:

The refractive index of the material of a glass prism is \( \sqrt{3} \). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

Two identical symmetric double convex lenses of focal length \( f \) are cut into two equal parts \( L_{1}\!, L_{2} \) by \( AB \) plane and \( L_{3}\!, L_{4} \) by \( XY \) plane as shown in figure respectively. The ratio of focal lengths of lenses \( L_{1} \) and \( L_{3} \) is:

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness \( 'h' \) in terms of the angle of incidence \( 'i' \) and angle of refraction \(' r '\), if the glass slab is placed in air medium?

Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below:

A hemispherical vessel is completely filled with a liquid of refractive index \( \mu \). A small coin is kept at the lowest point \( (O )\) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point \( E \) (at the level of the vessel) is ______.

A lens having refractive index \( 1.6 \) has focal length of \( 12 \, \text{cm} \), when it is in air. Find the focal length of the lens when it is placed in water: (Take refractive index of water as \( 1.28 \))

A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is \( 4D \) then the power of a part of the divided lens is:

Distance between object and its image (magnified by \( -\frac{1}{3} \)) is \( 30 \, \text{cm} \). The focal length of the mirror used is \( \left( \frac{x}{4} \right) \, \text{cm} \), where magnitude of value of \( x \) is ______.

A concave-convex lens of refractive index \( 1.5 \) and the radii of curvature of its surfaces are \( 30 \, \text{cm} \) and \( 20 \, \text{cm} \), respectively. The concave surface is upwards and is filled with a liquid of refractive index \( 1.3 \). The focal length of the liquid-glass combination will be:

At the interface between two materials having refractive indices \( n_1 \) and \( n_2 \), the critical angle for reflection of an em wave is \( \theta_{1C} \). The \( n_2 \) material is replaced by another material having refractive index \( n_3 \) such that the critical angle at the interface between \( n_1 \) and \( n_3 \) materials is \( \theta_{2C} \). If \( n_3 > n_2 > n_1 \); \( \frac{n_2}{n_3} = \frac{2}{5} \) and \( \sin \theta_{2C} - \sin \theta_{1C} = \frac{1}{2} \), then \( \theta_{1C} \) is:

A photograph of a landscape is captured by a drone camera at a height of \( 18 \,\text{km} \). The size of the camera film is \( 2 \,\text{cm} \times 2 \,\text{cm} \) and the area of the landscape photographed is \( 400 \,\text{km}^{2} \). The focal length of the lens in the drone camera is:

Let \( u \) and \( v \) be the distances of the object and the image from a lens of focal length \( f \). The correct graphical representation of \( u \) and \( v \) for a convex lens when \( |u| > f \), is:

A concave mirror produces an image of an object such that the distance between the object and image is \( 20 \, \text{cm} \). If the magnification of the image is \( '-3' \), then the magnitude of the radius of curvature of the mirror is:

When an object is placed \( 40 \, \text{cm} \) away from a spherical mirror an image of magnification \( \dfrac{1}{2} \) is produced. To obtain an image with magnification of \( \dfrac{1}{3} \), the object is to be moved:

A convex lens made of glass (refractive index \( = 1.5 \)) has focal length \( 24 \, \text{cm} \) in air. When it is totally immersed in water (refractive index \( = 1.33 \)), its focal length changes to:

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JEE MAIN 2025 4th April Morning Shift

Distance between object and its image (magnified by \( -\frac{1}{3} \)) is \( 30 \, \text{cm} \). The focal length of the mirror used is \( \left( \frac{x}{4} \right) \, \text{cm} \), where magnitude of value of \( x \) is ______.