Geometrical Optics — JEE Main PYQs

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

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 lev …

A thin prism ${\mathrm{P}}_1$ with angle $4^{\circ }$ made of glass having refractive index 1.54, is combined with another thin prism ${\mathrm{P}}_2$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism ${\mathrm{P}}_2$ in degrees …

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

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5 D ? ['D' stands for dioptre]

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 m. The radiu …

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of ${\mathrm{f}}_1$ in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of ${\mathrm{f}}_2$ when it is immersed in a liquid of refractive index 1. …

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

A bi-convex lens has radius of curvature of both the surfaces same as $1/6$ cm. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides (${\mathrm{R}}_1\ne {\mathrm{R}}_2$), without any change in lens power then possib …

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 ______.

The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm . The refractive index of the lens material is

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 emerge …

A monochromatic light of frequency $5\times 10^{14}\mathrm{Hz}$ travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be :

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 cm from the glass surface inside the glass. The magnitude of distance of the light source from …

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

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

Given below are two statements : one is 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 i …

A transparent block A having refractive index $\mu =1.25$ is surrounded by another medium of refractive index $\mu =1.0$ as shown in figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in figure. What is the maximum value of …

A lens having refractive index 1.6 has focal length of 12 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)

Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 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 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 cm. The value of H is _ …

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 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

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

For the thin convex lens, the radii of curvature are at 15 cm and 30 cm respectively. The focal length the lens is 20 cm . The refractive index of the material is :

A light ray is incident on a glass slab of thickness $4\sqrt{3}\mathrm{cm}$ and refractive index $\sqrt{2}$. The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ____ cm. …

An effective power of a combination of 5 identical convex lenses which are kept in contact along the principal axis is 25 D . Focal length of each of the convex lens is :

Given below are two statements :

Statement I: When the white light passed through a prism, the red light bends lesser than yellow and violet.

Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements …

Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is:

The refractive index of prism is $\mu =\sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is ______ ${}^{\circ }$.

Critical angle of incidence for a pair of optical media is $45^{\circ }$. The refractive indices of first and second media are in the ratio:

The position of the image formed by the combination of lenses is :

Given below are two statements:
Statement (I): When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side.
Statement (II): Concave lens always forms a virtual and erect image.
In the light of the …

The following figure represents two biconvex lenses ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ having focal length 10 cm and 15 cm respectively. The distance between ${\mathrm{L}}_1$ & ${\mathrm{L}}_2$ is :

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be :

If the refractive index of the material of a prism is $\cot \left(\frac{\mathrm{A}}{2}\right)$, where A is the angle of prism then the angle of minimum deviation will be

Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is 6 cm. A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is …

A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is:

A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

The refractive index of a prism with apex angle A is $\cot \mathrm{A}/2$. The angle of minimum deviation is :

The distance between object and its 3 times magnified virtual image as produced by a convex lens is 20 cm . The focal length of the lens used is ______ cm .

In an experiment to measure the focal length (f) of a convex lens, the magnitude of object distance ( x ) and the image distance ( y ) are measured with reference to the focal point of the lens. The y-x plot is shown in figure.

The focal length of the lens is ______ cm .

The distance between object and its two times magnified real image as produced by a convex lens is 45 cm. The focal length of the lens used is ______ cm.

Light from a point source in air falls on a convex curved surface of radius 20 cm and refractive index 1.5. If the source is located at 100 cm from the convex surface, the image will be formed at ______ cm from the object.

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance o …

In a reflecting telescope, a secondary mirror is used to:

Two vertical parallel mirrors A and B are separated by 10 cm. A point object O is placed at a distance of 2 cm from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ____ cm

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens ${\mathrm{L}}_1$ as show …

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